Find the middle term of (a/2 + 2b)⁶. Give the number of the middle term and its coefficient.

For even $n$ the middle term is $T_{n/2+1}$. For odd $n$ the middle terms are $T_{(n+1)/2}$ and $T_{(n+3)/2}$. The term free of $x$ has the power $0$ of $x$. For a small $x$, $(1 + x)^n \approx 1 + nx + \dfrac{n(n - 1)}{2}x^2 + \dots$