Let n be a positive integer. If the coefficients of 2nd, 3rd, and 4th terms in the expansion of (1+x)n are in AP, then the value of n is
The coefficients of 2nd, 3rd and 4th terms in the expansion of (1+x)n is nC1, nC2, nC3
According to the given condition,
2(nC2)=nC1+nC3⇒ 2n(n−1)1.2=n+n(n−1)(n−2)1.2.3⇒ n−1=1+(n−1)(n−2)6⇒ n−1=1+n2−3n+26⇒ 6n−6=6+n2−3n+2⇒ n2−9n+14=0⇒ (n−2)(n−7)=0⇒ n=2,7
But nC3 is true for n ≥ 3, therefore n = 7 is the answer.