Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: Rs.

There are no items in this cart.
Continue Shopping

Middle Term


(i) When n is even

Middle term of the expansion is the (n/2 + 1)th term

i.e. nCn/2 an/2 in the expansion of (a + b)n.

(ii) When n is odd

Middle terms of the expansion are the (n/2 + 1)th term and the ((n+3)/2)th term.

These are given by,nC((n-1)/2)  a((n+1)/2) a((n-1)/2) and nC((n+1)/2)  a((n-1)/2) a((n+1)/2)  in the expansion of (a + b)n.

e.g. middle term in the expansion of (1+x)4 and (1+x)5.

Expansion of (1+x)4 have 5 terms, so third term is the middle term which is the ((4/2)+1)th term.

Expansion of (1+x)5 have 6 terms, so 3rd and 4th both are the middle terms, which are the ((5+1)/2)th and ((5+3)/2)th terms.

  * rth term from the end = (n - r + 2)th term from the beginning. 
  * If there are two middle terms, then the binomial co-efficients of two middle terms will be equal and those two co-efficients will be greatest.


Find the middle term in the expansion of (1 - 2x + x2)n.


We have (1 - 2x + x2)n = [(1 -x)2]n = (1 - x)2n.

Here 2n is an even integer =>((2n/2) + 1)th i.e. (n+1)th term will be the middle term.

Now (n+1)th term in (1-x)2n = 2nCn (1)2n-n(-x)n = 2nCn(-x)n = (2n)!/n!n!

A comprehensive study material for IIT JEE, AIEEE and other engineering examinations is available online free of cost at Study Set Theory, Functions and a number of topics of Algebra at askIITians website. The website has links to numerous live online courses for IIT JEE preparation - you do not need to travel anywhere any longer - just sit at your home and study for IIT JEE live online with

To read more, Buy study materials of Binomial Theorem comprising study notes, revision notes, video lectures, previous year solved questions etc. Also browse for more study materials on Mathematics here.

  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: Rs. 15,000
  • View Details