Question

If the middle term in the expansion of ${(\frac{p}{2}+2)}^8$ is $1120$, then the value of $p$ is

• A. $\pm 2$
• B. $\pm 4$
• C. $\pm 1$
• D. $\pm 6$

Answer 1

The correct option is A $\pm 2$

Middle term of the given expansion will be $\frac{8}{2}+1=5^{\text{th}}$ term

$\therefore T_{4+1}={}^8{C}_4{\left(\frac{p}{2}\right)}^4\times 2^4\Rightarrow 1120=\frac{8\times 7\times 6\times 5}{4\times 3\times 2\times 1}\times \left(p^4\right)\Rightarrow p=\pm 2$