Precalculus (10th Edition)

$\sum_{k=0}^{n-1} ar^k$
We are given the sum: $a+ar+ar^2+...+ar^{n-1}$ The general term of the sum is $ar^k$. The number of terms is $n$, so the index $k$ goes from 0 to $n-1$. We write the sum: $a+ar+ar^2+...+ar^{n-1}=\sum_{k=0}^{n-1} ar^k$