The coefficients of three consecutive terms in the expansion of `(1+a)^n`are in the ratio 1: 7 : 42. Find n.

Explanation

To solve the problem of finding \( n \) given that the coefficients of three consecutive terms in the expansion of \( (1 + a)^n \) are in the ratio \( 1 : 7 : 42 \), we can follow these steps:

### Step 1: Identify the Coefficients
The coefficients of the \( r \)-th, \( (r+1) \)-th, and \( (r+2) \)-th terms in the expansion of \( (1 + a)^n \) are given by:
- Coefficient of \( r \)-th term: \( \binom{n}{r} \)
- Coefficient of \( (r+1) \)-th term: \( \binom{n}{r+1} \)
- Coefficient of \( (r+2) \)-th term: \( \binom{n}{r+2} \)

...