Question

# 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 ___ .

Solution

## 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.

Suggest corrections