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OlympiadBench / 2344 / The geometric sequence with n terms t₁,t₂,…,t_(n−1),t_(n) has…

Problem

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

answer type

Numerical

is multiple answer

false

language

English

question

The geometric sequence with

n

terms

t_{1}, t_{2}, \ldots, t_{n-1}, t_{n}

has

t_{1} t_{n}=3

. Also, the product of all

n

terms equals 59049 (that is,

t_{1} t_{2} \cdots t_{n-1} t_{n}=59049

). Determine the value of

n

. (A geometric sequence is a sequence in which each term after the first is obtained from the previous term by multiplying it by a constant. For example,

3,6,12

is a geometric sequence with three terms.)

Plain-text mathematical notation (without MathML)

The geometric sequence with n terms t₁,t₂,…,t_(n−1),t_(n) has t₁t_(n)=3. Also, the product of all n terms equals 59049 (that is, t₁t₂⋯t_(n−1)t_(n)=59049 ). Determine the value of n.

(A geometric sequence is a sequence in which each term after the first is obtained from the previous term by multiplying it by a constant. For example, 3,6,12 is a geometric sequence with three terms.)

Original LaTeX notation

The geometric sequence with $n$ terms $t_{1}, t_{2}, \ldots, t_{n-1}, t_{n}$ has $t_{1} t_{n}=3$. Also, the product of all $n$ terms equals 59049 (that is, $t_{1} t_{2} \cdots t_{n-1} t_{n}=59049$ ). Determine the value of $n$.

(A geometric sequence is a sequence in which each term after the first is obtained from the previous term by multiplying it by a constant. For example, $3,6,12$ is a geometric sequence with three terms.)

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2344
task_id: 534addeb-5fb9-5baf-8f20-a7c6f38f2a82
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2344
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

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