1962 AMC 12 Problem 3

Attempt Problem 3 of the 1962 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 1962 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

3.

The first three terms of an arithmetic progression are x−1,x-1, x+1,x+1, 2x+3,2x+3, in the order shown. The value of xx is:
−2-2
00
22
44
undetermined
Answer: B
Concepts:arithmetic sequencelinear equation
Small hint:
Consecutive differences in an arithmetic progression are equal
Big hint:
Set (x+1)−(x−1)(x+1)-(x-1) equal to (2x+3)−(x+1)(2x+3)-(x+1)
Solution:
Equality of consecutive differences gives 2=(2x+3)−(x+1)=x+2, 2=(2x+3)-(x+1)=x+2, so x=0.x=0.
Thus, the correct answer is B.
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