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OlympiadBench / 2266 / Determine all possible values of r such that the three term geometric sequence…

Problem

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

question

Determine all possible values of

r

such that the three term geometric sequence 4,

4 r, 4 r^{2}

is also an arithmetic sequence. (An arithmetic sequence is a sequence in which each term after the first is obtained from the previous term by adding a constant. For example, 3, 5, 7, 9, 11 is an arithmetic sequence.)

Plain-text mathematical notation (without MathML)

Determine all possible values of r such that the three term geometric sequence 4, 4r,4r² is also an arithmetic sequence.

(An arithmetic sequence is a sequence in which each term after the first is obtained from the previous term by adding a constant. For example, 3, 5, 7, 9, 11 is an arithmetic sequence.)

Original LaTeX notation

Determine all possible values of $r$ such that the three term geometric sequence 4, $4 r, 4 r^{2}$ is also an arithmetic sequence.

(An arithmetic sequence is a sequence in which each term after the first is obtained from the previous term by adding a constant. For example, 3, 5, 7, 9, 11 is an arithmetic sequence.)

answer type

Numerical

is multiple answer

false

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2266
task_id: 95f92ff4-438b-5538-a79f-0fa1648b7c3f
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2266
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

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