Second term of an arithmetic progression.

Algebra Level pending

Four positive integers form an arithmetic progression. If the product of the first and the last term is 70 70 and the second and the third term is 88 88 , what is the second term?


The answer is 8.

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2 solutions

Fletcher Mattox
Apr 27, 2021

There are two answers to this question. If the sequence is 14,11,8,5, then the answer is 11, not 8.

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Edwin Gray
Jul 10, 2018

Let the arithmetic progression be: a 1, a 1 + d, a 1 + 2d, a 1 + 3d. Then we have the 2 equations: (1) a 1 (a _ 1 + 3d) = 70, and (2) (a 1 + d)(a 1 + 2d) =88. Expanding and subtracting, 2d^2 = 18, or d = 3. then (1) becomes (a 1)^2 + 9a 1 - 70 = 0 , with solution a 1 = 5. So the second term is a_1 + d = 8. Ed Gray

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