In Exercises 1–8, write the first five terms of each geometric sequence. a1 = 20, 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. In this case, the first term is denoted as 'a1', and the common ratio 'r' determines how the sequence progresses.

First Term and Common Ratio

The first term of a geometric sequence is the initial value from which the sequence begins, represented as 'a1'. The common ratio 'r' is the factor by which each term is multiplied to obtain the next term. For example, if a1 = 20 and r = 1/2, each subsequent term is half of the previous term.

Finding Terms of a Sequence

To find the terms of a geometric sequence, you start with the first term and repeatedly multiply by the common ratio. For instance, starting with a1 = 20 and r = 1/2, the first five terms can be calculated as follows: 20, 20 * (1/2), 20 * (1/2)^2, and so on, resulting in the sequence 20, 10, 5, 2.5, 1.25.