Find a, b and n in the expansion of `(a+b)^n`if the first three terms of the expansion are 729, 7290 and 30375, respectively.

Explanation

To find the values of \( a \), \( b \), and \( n \) in the expansion of \( (a + b)^n \) given that the first three terms are 729, 7290, and 30375, we can follow these steps:

### Step 1: Write the expressions for the first three terms
The first three terms of the expansion \( (a + b)^n \) can be expressed as:
- First term \( T_1 = \binom{n}{0} a^n b^0 = a^n \)
- Second term \( T_2 = \binom{n}{1} a^{n-1} b^1 = n a^{n-1} b \)
- Third term \( T_3 = \binom{n}{2} a^{n-2} b^2 = \frac{n(n-1)}{2} a^{n-2} b^2 \)

...