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Question

If the coefficients of 5th,6th,7th terms of (1+x)n are in A.P., then n=

A
10
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B
12
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C
14
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D
15
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Solution

The correct option is C 14
In the expansion (1+x)n
5th term =nC4x4
6th term =nC5x5
7th term, nC6x6

Given coefficient of these terms are in A.P.
2nC5=nC4+nC6

2n!(n5)!5!=n!(n4)!4!+n!(n6)!6!

2(n5)5=1(n4)(n5)+16.5

2(n5)5=30+(n4)(n5)6.5(n4)(n5)

12(n4)=30+(n4)(n5)

(12n+5)(n4)=30

(17n)(n4)=30

n2+21n68=30

n2+21n98=0

n221n+98=0

n214n7n+98=0

(n14)(n7)=0n=14

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