How to Find Any Term of a Geometric Sequence

Last Updated: December 5, 2022 References

A geometric sequence is a sequence derived by multiplying the last term by a constant.^{[1]
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Research source} Geometric progressions have many uses in today's society, such as calculating interest on money in a bank account. So if you were wondering how exactly you would work out how much money you'll have in there in a few years, this article will help you find out.

Steps

1
Identify the first term in the sequence, call this number a.^{[2]
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2
Calculate the common ratio (r) of the sequence. It can be calculated by dividing any term of the geometric sequence by the term preceding it.^{[3]
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3
Identify the number of term you wish to find in the sequence. Call this number n.^{[4]
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- For example, if you wish to find the 8^th term in the sequence, then n = 8.
4
The n^th term is given by ar^n-1. Simply insert the values of a, r and n in this formula and evaluate the resulting expression to get the n^th term.^{[5]
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Community Q&A

Question

How do I find the nth term in the sequence 1, 2, 4, 7, 11?

Donagan

Top Answerer

You can't do it, because that is neither a geometric nor an arithmetic sequence.
Question

How do I get the first term in a geometric sequence?

Community Answer

Take this for example. If you have given a3 = 27 and r = 3, divide 27 by 3, which is 9. Divide again by 3 and get 3. Then you have a1 = 3, a2 = 9, and a3 = 27. If you know the constant and one term in the geometric sequence, you can calculate any other term in the sequence.
Question

How do I get the nth term in a geometric sequence if the first term isn't given?

Donagan

Top Answerer

If you are given any term in the sequence, treat it as if it's the first term, and proceed as usual from there. If you're not given any terms in the sequence, you cannot find the nth term.