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Question

If k is a positive integer such that 36+k,300+k,596+k are the squares of three consecutive terms of an arithmetic progression, then common difference of this A.P. is

A
±1
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B
±2
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C
±4
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D
None of these
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Solution

The correct option is C ±4
Let the 3 consecutive terms of AP be a - d, a, a + d
Given (ad)2=36+k ______ (1)
a2=300+k __________ (2)
(a+d)2=596+k ________ (3)
(1) + (3) 2(a2+d2)=2k+632
a2+d2=k+316 _____ (4)
from (2) & (4)
300+k+d2=k+316
d2=16d=±4

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