The nth term of an arithmetic progression (AP) is given by the formula:
An = a + (n-1)d

Where:
An is the nth term of the AP
a is the first term of the AP
n is the position of the term in the AP
d is the common difference between consecutive terms

In this case, the nth term of the AP is given by the formula:

An = 3^n * 2^n

To find the sum of the first n terms of the AP (Sn), we can use the formula:

Sn = (n/2)(2a + (n-1)d)

Step 1: Finding the first term (a) and the common difference (d)
To find the first term (a) and the common difference (d), we can substitute the values of n = 1 and n = 2 into the given formula:

When n = 1, A1 = 3^1 * 2^1 = 6
When n = 2, A2 = 3^2 * 2^2 = 36

Using these two equations, we can solve for a and d.

A1 = a + (1-1)d
6 = a

A2 = a + (2-1)d
36 = a + d

From the first equation, we find that a = 6. Substituting this value into the second equation, we can solve for d:

36 = 6 + d
d = 30

Therefore, the first term (a) is 6 and the common difference (d) is 30.

Step 2: Finding the sum of the first n terms (Sn)
Now that we have the values of a and d, we can calculate the sum of the first n terms (Sn) using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values of a = 6 and d = 30, we get:

Sn = (n/2)(2*6 + (n-1)*30)
Sn = (n/2)(12 + 30n - 30)
Sn = (n/2)(12 + 30n - 30)
Sn = (n/2)(-18 + 30n)

Hence, the sum of the first n terms (Sn) is given by (n/2)(-18 + 30n).

Conclusion:
The sum of the first n terms (Sn) of the given arithmetic progression, with the nth term defined by the formula 3^n * 2^n, is (n/2)(-18 + 30n).