benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / For any sequence of real numbers A=(a₁,a₂,a₃,…), define ΔA to be the sequence (a₂−a₁,a₃−a₂,a₄−a₃,…), whose n^(th) term is a_(n+1)−a_(n). Suppose that all of the terms of the sequen…

Problem

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

problem

For any sequence of real numbers A=(a1,a2,a3,…)A=(a_1,a_2,a_3,\ldots), define ΔA\Delta A to be the sequence (a2−a1,a3−a2,a4−a3,…)(a_2-a_1,a_3-a_2,a_4-a_3,\ldots), whose nthn^{\text{th}} term is an+1−ana_{n+1}-a_n. Suppose that all of the terms of the sequence Δ(ΔA)\Delta(\Delta A) are 11, and that a19=a92=0a_{19}=a_{92}=0. Find a1a_1.
Plain-text mathematical notation (without MathML)
For any sequence of real numbers A=(a₁,a₂,a₃,…), define ΔA to be the sequence (a₂−a₁,a₃−a₂,a₄−a₃,…), whose n^(th) term is a_(n+1)−a_(n). Suppose that all of the terms of the sequence Δ(ΔA) are 1, and that a₁₉=a₉₂=0. Find a₁.
Original LaTeX notation
For any sequence of real numbers $A=(a_1,a_2,a_3,\ldots)$, define $\Delta A$ to be the sequence $(a_2-a_1,a_3-a_2,a_4-a_3,\ldots)$, whose $n^{\text{th}}$ term is $a_{n+1}-a_n$. Suppose that all of the terms of the sequence $\Delta(\Delta A)$ are $1$, and that $a_{19}=a_{92}=0$. Find $a_1$.

level

Level 4

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
ff242ec2-8746-5a9e-875a-799c98c48815
task_key
intermediate~5falgebra--test--ff242ec2-8746-5a9e-875a-799c98c48815
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import