Middle term in the expansion of
Question:

Middle term in the expansion of (a3 + ba)28 is ___________.

Solution:

In (a3 + ba)28

Here n = 28

So, there is one middle term

i.e. $\left(\frac{28}{2}+1\right)$ th term which is 15 th term

$\therefore$ Middle term is $T_{15}$

i. e. $T_{14+1}={ }^{28} C_{14}\left(a^{3}\right)^{28-14}(b a)^{14} \quad$ (using $T_{r+1}={ }^{n} C_{r} x^{r} y^{n-r}$ for $\left.(x+y)^{n}\right)$

$={ }^{28} C_{14}\left(a^{3}\right)^{14} b^{14} a^{14}$

$={ }^{28} C_{14} a^{56} a^{14}$

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