If $a$ is a real number and if the middle term of ${\left(\frac{a}{3}+3\right)}^8$ is 1120, then value of $a$ is

Middle term of ${\left(\frac{a}{3}+3\right)}^8$ is the $\left(\frac{8}{2}+1\right)$ th or $5^{th}$ term. We have

$T_5=T_{4+1}{=}^8{C}_4{\left(\frac{a}{3}\right)}^4(3{)}^4=70a^4$

We are given $T_5=1120\Rightarrow 70a^4=1120$

$\Rightarrow a^4=16=2^4\Rightarrow a=\pm 2$