The common difference of the divisible byA. 1B. 3C. 2D. `-2` – InterviewSolution

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1.	The common difference of the divisible byA. 1B. 3C. 2D. `-2`
Answer» Correct Answer - A Let the four integers be a-d,a,a+d, and a+2d, where a and d are integers and `dgt0`. Now, `a+2d=(a-d)^(2)+a^(2)+(a+d)^(2)` or `2d^(2)-2d+3a^(2)-a=0` (1) `therefored=1/2[1pmsqrt(1+2a-6a^(2))]` (2) Since d is a positive integer, so `1+2a-6a^(2)gt0` or `6a^(2)-2a-1lt0` or `(1-sqrt7)/6ltalt(1+sqrt7)/6` or a=0 (`because` a is an integer) Hence, from (2), d=1 or 0 But since `dgt0`, `therefore` d=1 Hence, the four numbers are -1,0,1,2.

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