benchmarks.wiki

benchmarks.wiki / Public workspace

OlympiadBench / 2286 / Suppose that n>5 and that the numbers …

Problem

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

question

Suppose that n>5n>5 and that the numbers t1,t2,t3,…,tn−2,tn−1,tnt_{1}, t_{2}, t_{3}, \ldots, t_{n-2}, t_{n-1}, t_{n} form an arithmetic sequence with nn terms. If t3=5,tn−2=95t_{3}=5, t_{n-2}=95, and the sum of all nn terms is 1000 , what is the value of nn ? (An arithmetic sequence is a sequence in which each term after the first is obtained from the previous term by adding a constant, called the common difference. For example, 3,5,7,93,5,7,9 are the first four terms of an arithmetic sequence.)
Plain-text mathematical notation (without MathML)
Suppose that n>5 and that the numbers t₁,t₂,t₃,…,t_(n−2),t_(n−1),t_(n) form an arithmetic sequence with n terms. If t₃=5,t_(n−2)=95, and the sum of all n terms is 1000 , what is the value of n ?

(An arithmetic sequence is a sequence in which each term after the first is obtained from the previous term by adding a constant, called the common difference. For example, 3,5,7,9 are the first four terms of an arithmetic sequence.)
Original LaTeX notation
Suppose that $n>5$ and that the numbers $t_{1}, t_{2}, t_{3}, \ldots, t_{n-2}, t_{n-1}, t_{n}$ form an arithmetic sequence with $n$ terms. If $t_{3}=5, t_{n-2}=95$, and the sum of all $n$ terms is 1000 , what is the value of $n$ ?

(An arithmetic sequence is a sequence in which each term after the first is obtained from the previous term by adding a constant, called the common difference. For example, $3,5,7,9$ are the first four terms of an arithmetic sequence.)

answer type

Numerical

is multiple answer

false

language

English

question type

Open-ended

subject

Math

Discussion

Discussion

No discussion posts on this page yet. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. 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. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

Source and history

upstream_id / Original problem ID
2286
task_id
28d37915-a8e8-5ada-818b-b78313d789ba
task_key
OE~5fTO~5fmaths~5fen~5fCOMP--train--2286
task_revision_id
4
config / split
OE_TO_maths_en_COMP / train

Official source

initial import