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Geometric Sequence

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Geometric Sequence

by sal_xcool » Tue Mar 08, 2011 8:38 am
Do we need to know the geometric sequence sum formula for GMAT exam?

I haven't seen any questions that ask for it but would like some reassurance on this.

I would appreciate it if some experts could help me out on this.
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by Anurag@Gurome » Tue Mar 08, 2011 8:33 pm
It is not "necessary" to remember the formula, but you can easily derive it if a question requires its knowledge.

Let the geometric sequence be a, ar, ar^2, ar^3....
So the nth term is ar^(n-1).
Or the sum to n terms given by S = a + ar + ar^2 + ar^3 +...+ar^(n-2) + ar^(n-1).---------(1)
Now, multiply both sides of the equation by r and we get
Sr = ar + ar^2 + ar^3+...+ar^(n-1) + ar^n.-------------(2).
Subtracting (2) from (1), we get that S - Sr = a - ar^n (all other terms will cancel out).
Or S(1-r) = a(1 - r^n).
Or S = a(1 - r^n)/(1-r).
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