Questions
If the coefficients of 5th, 6th and 7th terms in the expansion of are in A.P., then n =
a
7 only
b
14 only
c
7 or 14
d
none of these
detailed solution
Correct option is C
Coefficient of T5 is nC4,that of T6 is nC5 and that of T7 is nC6. According to the condition, 2nC5=nC4+nC6.Hence,2n!(n−5)!5!=n!(n−4)!4!+n!(n−6)!6!or 21(n−5)5=1(n−4)(n−5)+16×5After solving, we get n = 7 or 14.Talk to our academic expert!
Similar Questions
If the coefficients of P th, ( p + 1)th and (p + 2)th terms in the expansion of (1 + x)n are in AP, then
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