Question

Which of the following values of n are possible, if the middle term of (x + 3y)^n is the fifth term.

(a) 6, 7 or 8

(b) 7, 8 or 10

(c) 7, 8 or 9

(d) 8, 9 or 10

The question was posed to me during an online interview.

I want to ask this question from Binomial Theorem in chapter Binomial Theorem of Mathematics – Class 11

Answer 1

The correct option is (c) 7, 8 or 9

Explanation: If n is the number of terms and is even, then the middle term is the \((\frac{n}{2} + 1)^{th}\) term.

Else if n is the number of terms and is odd, there are two middle terms which are the \((\frac{n + 1}{2})^{th}\) term and the \((\frac{n + 3}{2})^{th}\) term.

Case 1: \(\frac{n}{2} + 1\) = 5 ; n = 8

Case 2: \(\frac{n + 1}{2}\) = 5 ; n = 9

Case 3: \(\frac{n + 3}{2}\) = 5 ; n = 7