What and how is the geometric sequence formula, a(n) = a*r^(n-1) used for
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What and how is the geometric sequence formula, a(n) = a*r^(n-1) used for

[From: ] [author: ] [Date: 12-02-29] [Hit: ]
justr take the cirrent term and multiply it by r. This is also referred to as the generating formula.......
I have a test on this tomorrow and the way it's explained online is a bit confusing. If anyone can help, then please do so. I need to know what you would use this formula for, and how you would apply it to a problem. Also, what does each variable stand for?

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The formula gives you any specific term, given the first term, a, specified n, as well as the ratio: r.

So a(1) should be a. Let';s check it. a(1) = a•r ¹⁻¹= ar° = a(1) = a

The third term, for example would be a(3) = a•r³⁻¹ = ar²

Suppose a = 2 and r = ½,
a(1) = a = 2(½)° = 2(1) = 2 --- as it should be.

a(2) = 2(½)¹ = 1

a(3) = 2(½)² = 2(¼) = ½

And so it continues.

The kth term would be a(k) = 2(½)ᵏ⁻¹

There is also a related RECURSION formula which gives you each term computed from the previuos term. a(n+1) = a(n)•r This recursion formula just says to fid the next term, justr take the cirrent term and multiply it by r. This is also referred to as the generating formula.
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