Question

What is the term of a 7-term geometric series if the first term is -11 the last term is -45,056 and the common ratio is -4

Answer 1

I assume you mean to ask how to find the sum of the seven terms?

You have


`a_2=ra_1`

`a_3=ra_2=r^2a_1`

`a_4=ra_3=r^3a_1`
...

`a_7=ra_6=r^6a_1`

So the sum is


`a_1+ra_1+r^2a_1+\cdots+r^6a_1=a_1(1+r+r^2+\cdots+r^6)=a_1*(1-r^7)/(1-r)`

You know that
`a_1=-11` and
`r=-4`, so the sum is equal to


`-4*(1-(-4)^7)/(1-(-4))=-13108`