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Question

If the coefficients of rth,(r+1)th and (r+2)th terms in the expansion of (1+x)14 are in A.P., then value r can be

A
5
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B
12
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C
10
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D
9
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Solution

The correct option is D 9
Coefficients of rth,(r+1)th and (r+2)th terms are 14Cr1, 14Cr and 14Cr+1
If these coefficients are in A.P., then
2(14Cr)=14Cr1+14Cr+1
2(14)!r!(14r)!=(14)!(r1)!(15r)!+(14)!(r+1)!(13r)!
2(14)!r!(14r)!=(14)![(r+1)r+(15r)(14r)(r+1)!(15r)!
2(15r)(r+1)=2r228r+210
r214r+45=0
(r5)(r9)=0
r=5 or 9

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