Question

If the coeffecients of the 5th,6th and 7th terms in the expansion ${(1+x)}^n$ are in A.P., then $n$ is equal to

• A. 7 only
• B. 14 only
• C. 7 or 14
• D. none of these

Answer 1

The correct option is C 7 or 14

For the above given terms to be in A.P, r and n should have the following relationship.
$(n-2r{)}^2=(n+2)$
Here rth term is 5th.
Therefore $r=5.$
Substituting r=5 in the above expression.
$(n-10{)}^2=(n+2)$
$n^2-20n+100=n+2$
$n^2-21n+98=0$
$(n-7)(n-14)=0$
Hence n=7 or n=14