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 solve the problem, we need to find the values of \( a \), \( b \), and \( n \) in the expansion of \( (a+b)^n \) given that the first three terms of the expansion are 729, 7290, and 30375, respectively.

### Step 1: Write the first three terms of the binomial expansion
The first three terms of the expansion of \( (a+b)^n \) are given by:
1. First term: \( T_1 = \binom{n}{0} a^n b^0 = a^n \)
2. Second term: \( T_2 = \binom{n}{1} a^{n-1} b^1 = n a^{n-1} b \)
3. Third term: \( T_3 = \binom{n}{2} a^{n-2} b^2 = \frac{n(n-1)}{2} a^{n-2} b^2 \)

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