Question

How do you find `S_n` for the arithmetic series given `a_1=7`, d=-2, n=9?

Answer 1

`S_n=-9`

Explanation:

This is an arithmetic series whose first term is `7` and common difference is `-2` i.e. series is `7,5,3,1,-1,....`

As `S_n=n/2(2a+(n-1)d)`

we have `S_9=9/2(2xx7+(9-1)(-2))`

= `9/2xx(14-8xx2)=9/2xx(-2)=-9`