Question

Let ${(1+x^2)}^2{(1+x)}^n=\sum _{k=0}^{n+4}{a}_k{x}^k$ , If $a_1,a_2,a_3ϵ$ A.P. then the set of values of $n$ is

• A. $3,4,5$
• B. $5,6,7$
• C. $2,3,4$
• D. None of these.

Answer 1

Answer: (C)

$2,3,4$

$a_1=C_1$
$a_2=2+C_2$
$a_3=C_3+2\times C_1$
since $a_1,a_2,a_3$ are in AP
$2\times a_2=a_1+a_3$
$n^3-9\times n^2+26\times n-24=0$
roots of the above equation are $2,3,4$