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Common Ratio Formula

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,

  1. an is the nth term of the geometric progression.
  2. an−1 is the (n - 1)th term of the geometric progression.
  3. 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:

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

Answer:Common ratio, r = 3

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Pdf of Common Ratio Formula