QA – Placement Quizzes | Progressions | Question 13

x, 17, 3x – y2 – 2 and 3x + y2 – 30 are four consecutive terms of an increasing arithmetic sequence. The sum of the four numbers is divisible by:
(A) 2
(B) 3
(C) 5
(D) 7


Answer: (A)

Explanation: Let’s rewrite the 4 terms as
(17-d), 17, (17+d), (17+2d) where d is the common difference. Then,
Sum = (17-d) + 17 + (17+d) + (17+2d) = 17*4 + 2d = 2 * (17*2 + d).
So, their sum is divisible by 2.

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