Problem 88 - Algebra and Trigonometry

Question

What is a geometric sequence? Give an example with your explanation.

Step-by-Step Solution

Answer

A geometric sequence is a sequence in which each term after the first is obtained by multiplying the preceding term by a fixed, non-zero number known as the ratio. An example could be the sequence {2, 6, 18, 54, ...}, which has a ratio of 3.

Step 1: Definition

A geometric sequence is a sequence of numbers in which any term after the first is obtained by multiplying the preceding term by a fixed, non-zero number called the ratio, denoted as 'r'. This sequence can be expressed as: a, ar, ar^2, ar^3, ..., ar^n.

Step 2: Example

Take a sequence {2, 6, 18, 54, ...}. In this case, each term is created by multiplying the previous term by 3 (which is a non-zero number). Hence, this sequence is a geometric sequence, and the ratio is 3.