benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / Three distinct integers a, b, and c have the following properties:

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Three distinct integers a,a, b,b, and cc have the following properties: •\bullet abc=17955abc = 17955 •\bullet a,a, b,b, cc are three consecutive terms of an arithmetic sequence, in that order •\bullet 3a+b,3a + b, 3b+c,3b + c, 3c+a3c + a are three consecutive terms of a geometric sequence, in that order Find a+b+c.a + b + c.
Plain-text mathematical notation (without MathML)
Three distinct integers a, b, and c have the following properties:

• abc=17955

• a, b, c are three consecutive terms of an arithmetic sequence, in that order

• 3a+b, 3b+c, 3c+a are three consecutive terms of a geometric sequence, in that order

Find a+b+c.
Original LaTeX notation
Three distinct integers $a,$ $b,$ and $c$ have the following properties:

$\bullet$ $abc = 17955$

$\bullet$ $a,$ $b,$ $c$ are three consecutive terms of an arithmetic sequence, in that order

$\bullet$ $3a + b,$ $3b + c,$ $3c + a$ are three consecutive terms of a geometric sequence, in that order

Find $a + b + c.$

level

Level 5

type

Intermediate Algebra

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
8f0c2d7f-5177-5780-a20b-305a0db0aa66
task_key
intermediate~5falgebra--test--8f0c2d7f-5177-5780-a20b-305a0db0aa66
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import