1975 AMC 12 Problem 15
Attempt Problem 15 of the 1975 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1975 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
15.
In the sequence of numbers each term after the first two is equal to the term preceding it minus the term preceding that. The sum of the first one hundred terms of the sequence is
Answer: A
Small hint:
Generate terms until the initial pair returns
Big hint:
The six-term period has sum
Solution:
The sequence begins and repeats every terms, with period sum The first terms sum to and the last four sum to
Therefore, the correct answer is A.
Problem 15 in other years
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