Understanding the Common Ratio in Geometric Sequences: An Essential Guide for Math Enthusiasts

Common Ratio r

In mathematics, the term “common ratio” refers to the constant value by which each term of a geometric sequence is multiplied to obtain the next term

In mathematics, the term “common ratio” refers to the constant value by which each term of a geometric sequence is multiplied to obtain the next term. A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a fixed, non-zero value.

The common ratio, denoted by the letter “r”, can be positive, negative, or a fraction. To find the common ratio of a geometric sequence, you need to divide any term (other than the first term) by its previous term. If the sequence is given in explicit form, you can divide any term by the term with one position less to determine the common ratio.

For example, consider the following geometric sequence: 2, 6, 18, 54, …

To find the common ratio, we can divide any term by its previous term:
6 ÷ 2 = 3
18 ÷ 6 = 3
54 ÷ 18 = 3

In this case, the common ratio “r” is 3. This means that each term in the sequence is obtained by multiplying the previous term by 3.

Note that the common ratio can also be negative. For example, if the sequence is: -3, 6, -12, 24, …, the common ratio is -2. This indicates that each term is found by multiplying the previous term by -2.

To summarize, the common ratio “r” in a geometric sequence is the constant value by which each term is multiplied to obtain the next term.

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