Answer
arithmetic, $a_n=3(-2)^{n-1} $, $S_{10} =-1023 $
Work Step by Step
Given the sequence $3,-6,12,-24,48,...$, we have $\frac{-6}{3}-=-2, \frac{12}{-6}=-2,...$ and it can be identified as an arithmetic sequence. We have $a_n=3(-2)^{n-1} $ and $S_{10}=(3)\frac{1-(-2)^{10}}{1-(-2)}=-1023 $
