Question

$x, 17, 3x - y^2 - 2$, and $3x + y^2 - 30$, are four consecutive terms of an increasing arithmetic sequence. The sum of the four number is divisible by:

Accepted Answer

A. Let common difference be $d$. $d = 17 - x = (3x - y^2 - 2) - 17 = (3x + y^2 - 30) - (3x - y^2 - 2)$. Solving these equations yields $x = 13$ and $y^2 = 16$. The terms are $13, 17, 21, 25$. Sum $= 13 + 17 + 21 + 25 = 76$, which is divisible by 2.

Arithmetic Sequence Terms Divisibility

Explanation

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