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. **Formula used:** The $n$th term of a sequence, $a_n$, can be found using the sum formula: $$a_n = S_n - S_{n-1}$$ where $S_n$ is the sum of the first $n$ terms and $S_{n-1}$ is the sum of the first $n-1$ terms. 3. **Find $a_n$:** $$a_n = S_n - S_{n-1} = (n^2 + 3n) - ((n-1)^2 + 3(n-1))$$ 4. **Simplify $a_n$:** $$a_n = n^2 + 3n - (n^2 - 2n + 1 + 3n - 3)$$ $$a_n = n^2 + 3n - n^2 + 2n - 1 - 3n + 3$$ $$a_n = (3n + 2n - 3n) + (-1 + 3)$$ $$a_n = 2n + 2$$ 5. **Check if $a_n$ forms an AP:** The general term $a_n = 2n + 2$ is a linear function of $n$, which means the difference between consecutive terms is constant. 6. **Common difference $d$:** $$d = a_{n+1} - a_n = [2(n+1) + 2] - (2n + 2) = 2n + 2 + 2 - 2n - 2 = 2$$ 7. **Conclusion:** The terms of the sequence are $a_n = 2n + 2$, and since the common difference $d = 2$ is constant, the sequence is an arithmetic progression. **Final answer:** $$a_n = 2n + 2$$