Question

What is the sum of the first 7 terms of the series −8+16−32+64−... ?

Answer 1

`S_7=-344`

Explanation:

For a geometric series we have `a_n=ar^(n-1)` where `a="first term"`, `r="common ratio"` and `n=n^(th)` `"term"`

The first term is clearly `-8`, so `a=-8`

`r=a_2/a_1=16/-8=-2`

The sum of a geometric series is `S_n=a_1((1-r^n)/(1-r))`

`S_7=-8((1-(-2)^7)/(1-(-2)))=-8(129/3)=-8(43)=-344`