Question

I JUST NEED THE ANSWER. What is the sum 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

Sadly, you can't have just the answer.
\[\large\sum_{k=1}^nar^{k-1}=a\frac{1-r^n}{1-r}\]
The common ratio is \(r=-4\).

The first term occurs when \(k=1\), which would be
\[-11=ar^{1-1}~~\iff~~a=-11\]
So you have the following series and summ,
\[\large\sum_{k=1}^7(-11)(-4)^{k-1}=(-11)\frac{1-(-4)^7}{1-(-4)}\]
Well, let me correct myself: you *can* have the answer, just not the simplified version.