Grade 11 General Mathematics: Geometric Sequences

A geometric sequence, also known as a geometric progression, is a sequence of numbers in which each term after the first is obtained by multiplying the preceding term by a fixed, non-zero constant called the common ratio ($r$).

Common Ratio

The common ratio ($r$) is the fixed number multiplied to get from one term to the next in a geometric sequence. It is defined by the formula:
$r = \frac{a_n}{a_{n-1}}$

Numerical Example

Consider the sequence: $4, 8, 16, 32, 64, \dots$ To verify that the sequence is geometric and find its common ratio, compute the ratio between each pair of consecutive terms:
$\frac{8}{4} = 2$
$\frac{16}{8} = 2$
$\frac{32}{16} = 2$
$\frac{64}{32} = 2$ The sequence is geometric with a common ratio of $r = 2$