Answer
$S_{10}=-10$
Work Step by Step
We have to find $S_{10}$ for the sequence:
$2,-4,6,-8,10,-12, . . .$
We can split the sum into pairs.
$S_{10}=(a_1+a_2) + (a_3+a_4) + . . . + (a_9+a_{10})$
There will be 5 such pairs in total. In each pair the sum of the terms is $-2$. So $S_{10}=-2-2-2-2-2=5(-2)=-10$
