Common Ratio Formula

Let us review what the common ratio is before understanding the common ratio formula. The "common ratio" is the number multiplied (or divided) at each level of a geometric series, because dividing (that is, finding the ratio of) subsequent terms always yields this value. The common ratio formula is used to get the common ratio for a geometric progression.

What Is the Common Ratio Formula?

A geometric progression is represented in general as a₁, (a₁r), (a₁r₁), (a₁r₁), (a₁r₁),..., where a₁ is the first term of GP, a1r is the second term of GP, and r is the common ratio. As a result, the geometric expression's common ratio formula is,

Common Ratio Formula:

Common ratio, r=arⁿ/arⁿ⁻¹

where,

an is the nth term of the geometric progression.
an−1 is the (n - 1)th term of the geometric progression.
In the following section, we'll look at how the common ratio formula is used.

Solved examples based on Common Ratio Formula

Example: Find the common ratio for the geometric sequence 1, 2, 4, 8, 16,... using the common ratio formula.

Sol: To find the Common ratio, Dividing each term by the previous term to determine whether a common ratio exists.

2/1=4/2=8/4=16/8=2

Because there is a common multiple, 2, known as the common ratio, the sequence is geometric.

Answer: Common ratio, r = 2

Example: What is the common ratio for a geometric sequence whose formula for the nth term is given by: ann = 4(3)^n-1?

Sol:

To find the Common ratio, it is given that Formula of geometric sequence = 4(3)^n-1
A list of the terms will demonstrate what is occurring in the sequence (start with n = 1).
4, 12, 36,108,...
Using the common ratio formula,
r = 12/4 =

Answer:Common ratio, r = 3

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Common Ratio Formula