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MATH / The n^(th) term of a certain geometric series is given by a⋅r^(n−1), where a and r are positive integers and r is greater than 1. Bill picks out k different numbers in this sequenc…

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problem

The nthn^{\text{th}} term of a certain geometric series is given by a⋅rn−1a\cdot r^{n-1}, where aa and rr are positive integers and rr is greater than 1. Bill picks out kk different numbers in this sequence, all of which have the same number of digits. What is the largest possible value of kk?
Plain-text mathematical notation (without MathML)
The n^(th) term of a certain geometric series is given by a⋅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?
Original LaTeX notation
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 $k$?

level

Level 5

type

Algebra

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Source and history

task_id
a80204a7-20b8-52ba-b1ac-23e711f0d822
task_key
algebra--test--a80204a7-20b8-52ba-b1ac-23e711f0d822
task_revision_id
1
config / split
algebra / test

Official source

initial import