Explain how to find the sum of the first n terms of a geometric series.

To find the sum of the first n terms of a geometric series, use the formula Sn = a(1-r^n)/(1-r), where a is the first term, r is the common ratio, and n is the number of terms.

A geometric series is a sequence of numbers where each term is found by multiplying the previous term by a constant ratio. The sum of the first n terms of a geometric series can be found using the formula Sn = a(1-r^n)/(1-r), where a is the first term, r is the common ratio, and n is the number of terms.

To use this formula, first identify the values of a, r, and n. Then substitute these values into the formula and simplify. For example, consider the geometric series 2, 4, 8, 16, 32, ...

The first term is a = 2, and the common ratio is r = 4/2 = 2. To find the sum of the first 5 terms, n = 5. Substituting these values into the formula, we get:

Sn = a(1-r^n)/(1-r)
= 2(1-2^5)/(1-2)
= 2(-31)/(-1)
= 62

Therefore, the sum of the first 5 terms of the geometric series 2, 4, 8, 16, 32, ... is 62.

It is important to note that the formula for the sum of a geometric series only works if the common ratio is not equal to 1. If the common ratio is 1, then the series is simply a sequence of the same number repeated, and the sum of the first n terms is n times that number.