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

$a_1+ra_1+r^2a_1+\cdots+r^6a_1=a_1(1+r+r^2+\cdots+r^6)=a_1\times\dfrac{1-r^7}{1-r}$

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

$-4\times\dfrac{1-(-4)^7}{1-(-4)}=-13108$