Lesson 6.2 Geometric Sequences

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.

To find the first four terms, start with the first term and multiply by the common ratio for each subsequent term. For example, if a₁ = 10 and the common ratio is 3, the terms are: 10, 30, 90, 270.

The recursive rule for a geometric sequence is defined as: a₁ = first term; a_n = a_n-1 * r, where r is the common ratio.

The common ratio can be found by dividing any term by the previous term. For example, in the sequence 64, 16, 4, the common ratio is 1/4 (16/64 or 4/16).

In a geometric sequence, each term is multiplied by a constant (common ratio), while in an arithmetic sequence, each term is added to a constant (common difference).

To find the next term, multiply the last known term by the common ratio. For example, if the last term is 90 and the common ratio is 3, the next term is 90 * 3 = 270.