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# The $n^{\text{th}}$ term of a certain geometric series is given by $a\cdot r^{n-1}$, where $a$ and $r$ are positive integers and $r$ is

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The $n^{\text{th}}$ term of a certain geometric series is given by $a\cdot r^{n-1}$, where $a$ and $r$ are positive integers and $r$ is greater than 1. Bill picks out $k$ different numbers in this sequence, all of which have the same number of digits. What is the largest possible value of $k$?

michaelcai  Oct 5, 2017
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k=4

a=5, 50, ....

r=2, slowest going up

michaelcai  Oct 6, 2017