2015 AMC 8 Problem 18
Attempt Problem 18 of the 2015 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 2015 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
18.
An arithmetic sequence is a sequence in which each term after the first is obtained by adding a constant to the previous term. For example, is an arithmetic sequence with five terms, in which the first term is and the constant is added. Each row and each column in this array is an arithmetic sequence with five terms. What is the value of
Answer: B
Small hint:
In a five-term arithmetic sequence, the middle term is the average of the first and last terms.
Big hint:
Apply that fact to the top row, bottom row, and then the middle column.
Video solution:
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Written solution:
In any five-term arithmetic sequence, the middle term is the average of the first and last terms.
The middle entry of the top row is and the middle entry of the bottom row is
Now apply the same fact to the middle column:
Thus, B is the correct answer.
Problem 18 in other years
- 1985 AMC 8
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