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Finite GP with unknown index

Authors
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    Name
    Vu Hung
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Problem Statement

For the geometric sequence with first term 55 and ratio 22, find nn such that

Sn=2555.S_n=2555.

Solutions

Sn=52n−12−1=5(2n−1)=2555.S_n=5\frac{2^n-1}{2-1}=5(2^n-1)=2555.

So

2n−1=511  ⟹  2n=512=29.2^n-1=511 \implies 2^n=512=2^9.

Hence n=9n=9.

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