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MATH / A strictly increasing sequence of positive integers a₁, a₂, a₃, … has the property that for every positive integer k, the subsequence a_(2k−1), a_(2k), a_(2k+1) is geometric and th…

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problem

A strictly increasing sequence of positive integers a1a_1, a2a_2, a3a_3, …\dots has the property that for every positive integer kk, the subsequence a2k−1a_{2k-1}, a2ka_{2k}, a2k+1a_{2k+1} is geometric and the subsequence a2ka_{2k}, a2k+1a_{2k+1}, a2k+2a_{2k+2} is arithmetic. Suppose that a13=2016a_{13} = 2016. Find a1a_1.
Plain-text mathematical notation (without MathML)
A strictly increasing sequence of positive integers a₁, a₂, a₃, … has the property that for every positive integer k, the subsequence a_(2k−1), a_(2k), a_(2k+1) is geometric and the subsequence a_(2k), a_(2k+1), a_(2k+2) is arithmetic. Suppose that a₁₃=2016. Find a₁.
Original LaTeX notation
A strictly increasing sequence of positive integers $a_1$, $a_2$, $a_3$, $\dots$ has the property that for every positive integer $k$, the subsequence $a_{2k-1}$, $a_{2k}$, $a_{2k+1}$ is geometric and the subsequence $a_{2k}$, $a_{2k+1}$, $a_{2k+2}$ is arithmetic. Suppose that $a_{13} = 2016$. Find $a_1$.

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
3885c1d7-0c81-5e99-8e84-5f613209ac45
task_key
intermediate~5falgebra--test--3885c1d7-0c81-5e99-8e84-5f613209ac45
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import