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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_9 / The sequence a₀,a₁,a₂,⋯ is a strictly increasing arithmetic sequence of positive integers such that 2^(a₇)=2²⁷⋅a₇. What is the minimum possible value of a₂?

Problem

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problem

The sequence

a_0,a_1,a_2,\cdots

is a strictly increasing arithmetic sequence of positive integers such that

2^{a_7}=2^{27} \cdot a_7.

What is the minimum possible value of

a_2

Plain-text mathematical notation (without MathML)

The sequence a₀,a₁,a₂,⋯ is a strictly increasing arithmetic sequence of positive integers such that 2^(a₇)=2²⁷⋅a₇. What is the minimum possible value of a₂?

Original LaTeX notation

The sequence $a_0,a_1,a_2,\cdots$ is a strictly increasing arithmetic sequence of positive integers such that \[2^{a_7}=2^{27} \cdot a_7.\] What is the minimum possible value of $a_2$?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_9
task_id: 8b6a5607-b3a9-5578-ac4e-6ef46feeb14a
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f9
task_revision_id: 2
config / split: default / train

Official source

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