Chapter 11 - Further Topics in Algebra - Summary Exercises on Sequences and Series - Exercises - Page 1038: 16

arithmetic, $a_n= -3n-2 $, $S_{10}= -185 $

Given the sequence $-5,-8,-11,-14,-17,...$, we have $-8-(-5)=-3, -11-(-8)=-3,...$ and it can be identified as an arithmetic sequence. We have $a_n=-5+(n-1)(-3)=-3n-2 $ and $S_{10}=\frac{10}{2}(-5-3(10)-2)=-185 $