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

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

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant factor, called the common ratio. For example, the sequence 2, 4, 8, 16, 32 is a geometric sequence with a first term of 2 and a common ratio of 2.

To find the sum of the first n terms of a geometric sequence, use the formula Sn = a(1 - r^n) / (1 - r), where a is the first term and r is the common ratio. For example, to find the sum of the first 5 terms of the sequence 2, 4, 8, 16, 32, we have a = 2 and r = 2, so Sn = 2(1 - 2^5) / (1 - 2) = 62.

It is important to note that this formula only works for finite geometric sequences, where the common ratio is not equal to 1. If the common ratio is equal to 1, the sequence is not geometric and the sum of the first n terms is simply n times the first term. If the common ratio is greater than 1, the sequence is increasing and the sum of the first n terms will approach infinity as n approaches infinity. If the common ratio is between -1 and 1, the sequence is decreasing and the sum of the first n terms will approach the limit of a / (1 - r) as n approaches infinity.