From 1984 to 2016

Algebra Level 2

An infinite geometric sequence has a first term of 1984, and all the terms in the sequence sum to 2016. What is the common ratio of the geometric sequence?

The answer can be expressed as a b \dfrac ab for coprime positive integers a a and b b , find a + b a+b .


The answer is 64.

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Paul Fournier by Paul Fournier , 70, Canada

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2 solutions

Atul Shivam
Jan 13, 2016

given a = 1984 a=1984 , S = 2016 S=2016 now 1984 1 − r = 2016 \frac{1984}{1-r}=2016 hence r = 32 2016 = 1 63 r=\frac{32}{2016}=\frac{1}{63} so the correct answer is 1 + 63 = 64 1+63=\boxed{64}

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Prasath M
Jan 14, 2016

the same way!

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