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, 2007

Algebra Difficulty 2.0 Junior Prove it Canada

Sequence A has $n$ th term $n^2-10n+70$ . (The first three terms of sequence A are 61, 54, 49.) Sequence B is an arithmetic sequence with first term 5 and common difference 10. (The first three terms of sequence B are 5, 15, 25.) Determine all $n$ for which the $n$ th term of sequence A is equal to the $n$ th term of sequence B. Explain how you got your answer.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.