Question

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

Geometric series:
\[a+ar+ar^2+ar^3+... \]
If there are 7 terms:
\[\sum_{n=1}^7ar^{n-1}=a+ar+ar^2+...+ar^6 \]

First term: \(a=-11\)
Last term: \(ar^6=-45,056\)
But \(r=-4\)

So you can add these individually as: \(-11+(-11)(-4)+(-11)(-4)^2+...+(-11)(-4)^6\)
Or the formula which is easier:
\[ a\left(\frac{1-r^n}{1-r} \right)\]