1. **State the problem:** We are given the sum of the first $n$ terms of a sequence as $S_n = n^2 + 3n$. We need to find the terms of the sequence and check if it forms an arithmetic progression (AP). 2. **Recall the formula:** The $n$th term $a_n$ of a sequence can be found from the sum $S_n$ by the formula: $$a_n = S_n - S_{n-1}$$ where $S_0 = 0$. 3. **Calculate the first term:** $$a_1 = S_1 - S_0 = (1^2 + 3 \times 1) - 0 = 1 + 3 = 4$$ 4. **Calculate the general term:** $$a_n = S_n - S_{n-1} = (n^2 + 3n) - ((n-1)^2 + 3(n-1))$$ 5. **Simplify the expression:** $$a_n = n^2 + 3n - (n^2 - 2n + 1 + 3n - 3) = n^2 + 3n - n^2 + 2n - 1 - 3n + 3$$ 6. **Combine like terms:** $$a_n = (3n - 3n + 2n) + (-1 + 3) = 2n + 2$$ 7. **Check if the sequence is arithmetic:** The $n$th term is $a_n = 2n + 2$. The difference between consecutive terms is: $$a_{n+1} - a_n = [2(n+1) + 2] - (2n + 2) = 2n + 2 + 2 - 2n - 2 = 2$$ Since the difference is constant, the sequence is an arithmetic progression with common difference 2. **Final answer:** The terms of the sequence are given by $$a_n = 2n + 2$$ which form an arithmetic progression with common difference 2.