Problem:
Consider the arithmetic sequence defined by $a_1=\frac{49}{40}$, and $a_n=a_{n-1}+-6 \sqrt{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\sum_{k=1}^n a_k$, where $n=19$.
Answer:
$\frac{19}{2} \left(\frac{49}{20}-108 \sqrt{2}\right)$
{'source': 'AMPS', 'file': 'amps/mathematica/algebra/arithmetic_series/5161.txt'}