Finding Sums of Finite and Infinite Geometric Series

Sum of a finite geometric series

For a finite geometric series with n terms, first term a, and common ratio r, the sum S_n is S_n = a (1 - r^n) / (1 - r), as long as r ≠ 1.

Sum of an infinite geometric series

For an infinite geometric series with first term a and common ratio |r| < 1, the sum S is S = a / (1 - r).

First term in a geometric series

a is the first term of the series, the starting value from which each term is multiplied by the common ratio r to obtain the next term.