In the binomial expansion of `(1+x)^n` , coefficients of the fifth, sixth and seventh terms are in A.P. find all the values of `n` for which this can happen.

Explanation

To solve the problem, we need to find the values of \( n \) for which the coefficients of the fifth, sixth, and seventh terms in the binomial expansion of \( (1+x)^n \) are in Arithmetic Progression (A.P.).

### Step-by-Step Solution:

1. **Identify the Terms**:
The \( r \)-th term in the binomial expansion of \( (1+x)^n \) is given by:
\[
T_r = \binom{n}{r-1} x^{r-1}
...