If the coefficients of 5th, 6th , and 7th terms in the expansion of `(1+x)^n` are in A.P., then `n=` a. 7 only b. 14 only c. 7 or 14 d. none of these

Options

A. 7 only
B. 14 only
C. 7 or 14
D. none of these

Explanation

To solve the problem, we need to find the value of \( n \) such that the coefficients of the 5th, 6th, and 7th terms in the expansion of \( (1+x)^n \) are in Arithmetic Progression (AP).

### Step-by-Step Solution:

1. **Identify the coefficients of the terms**:
The coefficients of the 5th, 6th, and 7th terms in the expansion of \( (1+x)^n \) are given by:
- 5th term: \( T_5 = \binom{n}{4} \)
- 6th term: \( T_6 = \binom{n}{5} \)
...