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[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=0$, and $a_n=a_{n-1}+\\frac{17}{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=27$."...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{48}{49}$, and $a_n=a_{n-1}+4$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=24$...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{24}{59}$, and $a_n=a_{n-1}+2 \\sqrt{3}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{7}{4}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=10$."...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{12}{29}$, and $a_n=a_{n-1}+-\\frac{11}{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, ...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{38}{69}$, and $a_n=a_{n-1}+\\frac{13}{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, ...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{62}{99}$, and $a_n=a_{n-1}+\\frac{13}{\\sqrt{3}}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=0$, and $a_n=a_{n-1}+4$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=20$." }, { ...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{8}{9}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=4$." ...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{1}{4}$, and $a_n=a_{n-1}+10$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=4$." ...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{39}{28}$, and $a_n=a_{n-1}+-6$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=27...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{10}{11}$, and $a_n=a_{n-1}+-6$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=20...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{1}{85}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=23$."...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{99}{92}$, and $a_n=a_{n-1}+4 \\sqrt{5}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{14}{45}$, and $a_n=a_{n-1}+-3$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=14$...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{31}{21}$, and $a_n=a_{n-1}+\\frac{13}{\\sqrt{5}}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{37}{35}$, and $a_n=a_{n-1}+6$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=23$....
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{23}{38}$, and $a_n=a_{n-1}+-5$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=3$...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{23}{65}$, and $a_n=a_{n-1}+-6 \\sqrt{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, w...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{2}{3}$, and $a_n=a_{n-1}+10$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=26$."...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{19}{43}$, and $a_n=a_{n-1}+3$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=26$....
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{17}{7}$, and $a_n=a_{n-1}+10$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=11$....
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{10}{13}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=4$."...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{64}{67}$, and $a_n=a_{n-1}+-3$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=17...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{9}{35}$, and $a_n=a_{n-1}+\\frac{9}{\\sqrt{2}}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n ...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{81}{13}$, and $a_n=a_{n-1}+-6$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=22...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{1}{35}$, and $a_n=a_{n-1}+-\\frac{17}{\\sqrt{3}}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-8$, and $a_n=a_{n-1}+8$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=12$." }, { ...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{4}{89}$, and $a_n=a_{n-1}+\\frac{3}{5}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, whe...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{10}{3}$, and $a_n=a_{n-1}+-\\sqrt{5}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{32}{77}$, and $a_n=a_{n-1}+5$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=18$...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{2}{7}$, and $a_n=a_{n-1}+-5$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=25$."...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{91}{59}$, and $a_n=a_{n-1}+7$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=3$....
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{36}{89}$, and $a_n=a_{n-1}+\\sqrt{3}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wher...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{10}{13}$, and $a_n=a_{n-1}+6 \\sqrt{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, whe...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{1}{2}$, and $a_n=a_{n-1}+-\\frac{13}{3}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{19}{12}$, and $a_n=a_{n-1}+-8$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=7$....
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{45}{7}$, and $a_n=a_{n-1}+3 \\sqrt{5}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wher...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{17}{40}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=7$."...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{46}{87}$, and $a_n=a_{n-1}+-\\frac{5}{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, w...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{55}{61}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=6$."...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{6}{73}$, and $a_n=a_{n-1}+-\\frac{24}{7}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, w...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-3$, and $a_n=a_{n-1}+\\frac{24}{5}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=18$....
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{26}{23}$, and $a_n=a_{n-1}+2 \\pi$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-10$, and $a_n=a_{n-1}+-7$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=9$." }, { ...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{8}{13}$, and $a_n=a_{n-1}+-2 \\sqrt{5}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{53}{86}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=15$...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{61}{49}$, and $a_n=a_{n-1}+-5$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=27...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{15}{16}$, and $a_n=a_{n-1}+9$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=14$...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{4}{23}$, and $a_n=a_{n-1}+\\frac{5}{4}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, whe...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{47}{13}$, and $a_n=a_{n-1}+-8$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=9$...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{70}{37}$, and $a_n=a_{n-1}+-4 \\sqrt{5}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{11}{6}$, and $a_n=a_{n-1}+-6$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=26$...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{69}{79}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=30$...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{44}{37}$, and $a_n=a_{n-1}+10$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=7$....
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{11}{79}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=29$....
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{32}{5}$, and $a_n=a_{n-1}+3 \\pi$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{1}{71}$, and $a_n=a_{n-1}+-\\frac{19}{\\sqrt{5}}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{72}{5}$, and $a_n=a_{n-1}+-\\pi$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{17}{10}$, and $a_n=a_{n-1}+-6$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=7$...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{21}{47}$, and $a_n=a_{n-1}+-3 \\sqrt{5}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{62}{3}$, and $a_n=a_{n-1}+\\frac{10}{\\sqrt{3}}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n ...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{34}{41}$, and $a_n=a_{n-1}+5$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=29$....
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{29}{7}$, and $a_n=a_{n-1}+-2 \\sqrt{5}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{65}{28}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=23$....
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{15}{43}$, and $a_n=a_{n-1}+3$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=3$."...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{1}{3}$, and $a_n=a_{n-1}+\\frac{29}{7}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{41}{9}$, and $a_n=a_{n-1}+-6$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=16$....
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{78}{67}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=22$...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{46}{3}$, and $a_n=a_{n-1}+3 \\sqrt{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wher...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{73}{81}$, and $a_n=a_{n-1}+4$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=6$."...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{19}{37}$, and $a_n=a_{n-1}+\\frac{20}{3}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, w...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{37}{20}$, and $a_n=a_{n-1}+-\\frac{7}{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, w...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{9}{98}$, and $a_n=a_{n-1}+-5 \\sqrt{3}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, whe...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{1}{5}$, and $a_n=a_{n-1}+4$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=14$." ...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=15$, and $a_n=a_{n-1}+-\\frac{37}{7}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=10$...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{69}{86}$, and $a_n=a_{n-1}+3$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=23$....
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{51}{83}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=15$...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{87}{82}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=7$."...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{22}{43}$, and $a_n=a_{n-1}+-10$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=20...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{73}{15}$, and $a_n=a_{n-1}+4 \\sqrt{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{9}{37}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=9$." ...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{20}{9}$, and $a_n=a_{n-1}+2$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=8$." ...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{29}{6}$, and $a_n=a_{n-1}+\\frac{7}{3}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{17}{72}$, and $a_n=a_{n-1}+\\frac{13}{\\sqrt{2}}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{1}{7}$, and $a_n=a_{n-1}+-4 \\sqrt{5}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wher...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{11}{10}$, and $a_n=a_{n-1}+\\frac{55}{7}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, ...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{35}{31}$, and $a_n=a_{n-1}+-8$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=3$...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{2}{3}$, and $a_n=a_{n-1}+-\\frac{7}{3}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, whe...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{5}{43}$, and $a_n=a_{n-1}+4 \\sqrt{3}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wher...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{12}{37}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=13$....
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{7}{5}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=13$." ...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{29}{48}$, and $a_n=a_{n-1}+4$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=3$....
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{32}{23}$, and $a_n=a_{n-1}+-9$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=15...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{35}{41}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=25$....
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{43}{42}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=14$....
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{27}{5}$, and $a_n=a_{n-1}+1$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=26$....
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=6$, and $a_n=a_{n-1}+-3 \\sqrt{5}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=8$." ...
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=-\\frac{33}{50}$, and $a_n=a_{n-1}+6$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=6$....
algebra
arithmetic_series
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Consider the arithmetic sequence defined by $a_1=\\frac{78}{79}$, and $a_n=a_{n-1}+7$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=20$....
algebra
arithmetic_series