6. Middle Term in the Binomial Theorem: Let us now find the Middle Terms in our binomial expansion: (x + y)^{n} Two cases arise depending on index n. Case 1: when n is odd: There are two middle terms in Binomial Theorem. One is T_{( n + 1)/2} and the other is T_{( n + 3)/2} For eg,
if the binomial index n is 5, an odd number, then the two middle terms are:

The above method is somewhat round about. Let us see a more simple and straight way of finding middle term in Binomial Theorem.
If index n is 5, then number of terms is 6.
So, the two middle terms are (6/2)^{th} term i.e., 3^{rd} term which is T_{3} And the immediately next term namely (6/2)^{th}+1 i.e.,
4^{th} term which is T_{4} Note: Here, you should note that 6 stands for number of terms in the binomial expansion, and not the index n. Index n is 5 here. Case 2: when n is even: When the binomial index n is even, we can see there is only one middle term. And it is T_{( n/2 + 1)}
For example,
if index n = 6, an even number, then the middle term will be

T_{( n/2 + 1)} = T_{( 6/2 + 1)} = T_{4}

And you know how to find this middle term with the method of number of terms in the expansion. I leave that method to you to avoid confusion by discussing two methods. It is always better to stick to one method. With practice, that one method becomes a second nature and occurs to the mind lightning fast. With two methods in mind, the mind gets indecisive as to use which one of
the two.