Answer
$S_{10}=5$
Work Step by Step
We have to find $S_{10}$ for the sequence:
$-1,2,-3,4,-5,6, . . .$
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 equal $1$. So
$S_{10}=1+1+1+1+1=5$
