2023 AMC 8 Problem 22
Attempt Problem 22 of the 2023 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2023 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
22.
In a sequence of positive integers, each term after the second is the product of the previous two terms. The sixth term in the sequence is What is the first term?
Answer: D
Small hint:
Write the first several terms using first term and second term
Big hint:
The sixth term is
Video solution:
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Written solution:
Let be the first term and be the second.
Then we get the following sequence: Thus
Factoring gives Because and are positive integers, the only fifth powers that divide are and
If then which is impossible because is not a perfect cube. Therefore, and
This forces to equal
Thus, D is the correct answer.
Problem 22 in other years
- 1985 AMC 8
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