In Exercises 31–34, write the first five terms of each geometric sequence. a1 = 1/2, r = 1/2

Key Concepts

Geometric Sequence

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. This type of sequence is characterized by its exponential growth or decay, depending on whether the common ratio is greater than or less than one.

First Term (a1)

The first term of a geometric sequence, denoted as a1, is the initial value from which the sequence begins. In this case, a1 = 1/2 indicates that the first term of the sequence is one-half, which serves as the foundation for calculating subsequent terms.

Common Ratio (r)

The common ratio, denoted as r, is the factor by which each term in a geometric sequence is multiplied to obtain the next term. In this problem, r = 1/2 means that each term is half of the previous term, leading to a sequence that decreases progressively.