To find the value of n in the expansion of (x + a)^n, we can use the binomial theorem. According to the binomial theorem, the kth term in the expansion is given by the formula:

Tk = nCk * x^(n-k) * a^k

where nCk represents the binomial coefficient, which is the number of ways to choose k items from a set of n items.

Given that the first three terms in the expansion are 729, 7290, and 30375, we can use this information to solve for n.

Step 1: Finding the first term
The first term in the expansion is given by T0 = nC0 * x^n * a^0 = x^n.
Given that the first term is 729, we have:

x^n = 729

Step 2: Finding the second term
The second term in the expansion is given by T1 = nC1 * x^(n-1) * a^1 = n * x^(n-1) * a.
Given that the second term is 7290, we have:

n * x^(n-1) * a = 7290

Step 3: Finding the third term
The third term in the expansion is given by T2 = nC2 * x^(n-2) * a^2 = (n * (n-1) / 2) * x^(n-2) * a^2.
Given that the third term is 30375, we have:

(n * (n-1) / 2) * x^(n-2) * a^2 = 30375

Step 4: Solving the equations
We now have a system of equations with three unknowns: n, x, and a. However, we are only interested in finding the value of n.

By dividing the equation for the second term by the equation for the first term, we can eliminate x:

(n * x^(n-1) * a) / (x^n) = 7290 / 729

Simplifying this equation gives us:

n * (1/x)^(n-1) * a = 10

Similarly, by dividing the equation for the third term by the equation for the second term, we can eliminate a:

((n * (n-1) / 2) * x^(n-2) * a^2) / (n * x^(n-1) * a) = 30375 / 7290

Simplifying this equation gives us:

(n-1) * (1/x) * a = 15

Step 5: Simplifying the system of equations
Now we have two equations involving n, x, and a:

Equation 1: n * (1/x)^(n-1) * a = 10
Equation 2: (n-1) * (1/x) * a = 15

We can solve this system of equations to find the value of n.

By dividing Equation 2 by Equation 1, we get:

((n-1) * (1/x) * a) / (n * (1/x)^(n-1) * a) = 15 / 10

Simplifying this equation gives us:

(n-1) / n = 3/2