x, 17, 3x – y2 – 2, and 3x + y2 – 30, are four consecutive terms of an increasing arithmetic sequence. The sum of the four number is divisible by:
Explanation:
Since it is an A.P.,
Therefore, 17 – x = 3x + y2 – 30 – 3x + y2 + 2
Or, x + 2y2 = 45 … (i)
Again, 17 − x = 3x − y2 − 2 −17
Or, 4x – y2 = 36 … (ii)
Solving equations (i) and (ii),
we get x = 13.
Sum of the A.P. = x + 17 + 3x – y2 – 2 + 3x + y2 – 30
= 7x – 15 = 7(13) – 15 = 76
Out of the given options, 76 is only divisible by 2.
Hence, option (a).
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