Questions
If the coefficient of second, third and fourth terms in the expansion of (1 + x)2n are in AP, then 2n2 - 9n is equal to
a
-7
b
7
c
-6
d
6
detailed solution
Correct option is A
The general term of (1+x)2n is Tr+1=2nCrxrT2=2nC1x2,T3=2nC2x3,T4=2nC3x4Since , coefficients are in Ap.⇒ 2nC1,2nC2,2nC3 are in AP⇒ 2×2nC2=2nC1+2nC3⇒ 2= 2nC1 2nC2+ 2nC3 2nC2⇒ 2=2(2n−2+1)+2n−3+13⇒ 2=22n−1+2n−23⇒ 2n2−9n+7=0∴ 2n2−9n=−7Talk to our academic expert!
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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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