College Algebra & Trigonometry, 2018a

6.4. SUM OF A SERIES 301
Factor out S n on the left-hand side:
S n (1 − r) =a − ar n
and divide on both sides to isolate S n :
S n (1 − r)
(1 − r)
= a − arn
(1 − r)
S n = a − arn
1 − r
So for a finite geometric series, we can use this formula to find the sum. This
formula can also be used to help find the sum of an infinite geometric series, if
the series converges. Typically this will be when the value of r is between −1 and
1. In other words, |r| < 1 or −1