Solution:

Finding the nth term of the given AP:
The nth term of an AP is given by the formula: \(a_n = a_1 + (n-1)d\), where \(a_n\) is the nth term, \(a_1\) is the first term, n is the term number, and d is the common difference.
Given that the nth term is \(2 + \frac{1}{2}\), we can equate it to the formula:
\(2 + \frac{1}{2} = a_1 + (n-1)d\)
Simplifying the above equation gives:
\(2.5 = a_1 + (n-1)d\)
Since the first term is \(a_1\), we have:
\(a_1 = 2.5 - (1-1)d\)
\(a_1 = 2.5\)
Therefore, the first term of the AP is 2.5.

Finding the common difference:
From the nth term formula, we know that the common difference is the coefficient of n.
Hence, the common difference is 0.5.

Finding the sum of the first 30 terms:
The sum of the first n terms of an AP is given by the formula:
\(S_n = \frac{n}{2}(2a_1 + (n-1)d)\)
Substitute the values of n = 30, \(a_1 = 2.5\), and d = 0.5 into the formula, we get:
\(S_{30} = \frac{30}{2}(2(2.5) + (30-1)(0.5))\)
\(S_{30} = 15(5 + 14(0.5))\)
\(S_{30} = 15(5 + 7)\)
\(S_{30} = 15(12)\)
\(S_{30} = 180\)
Therefore, the sum of the first 30 terms of the given AP is 180.