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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