Maths Olympiad Prep

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, 2011

Algebra Difficulty 1.0 Junior Prove it Canada

An arithmetic sequence is a sequence in which each term after the first is obtained from the previous term by adding a constant dd, called the common difference. For example, 2,5,8,11,142, 5, 8, 11, 14 are the first five terms of an arithmetic sequence with a common difference of d=3d = 3.

(a) Determine the 6th6^{th} and 7th7^{th} terms of the sequence given above.

(b) What is the 31st31^{st} term in this sequence?

(c) If the last term in this sequence were 110, how many terms would there be in the sequence?

(d) If this sequence is continued, does 1321 appear in the sequence? Explain why or why not.

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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.