1. Problem statement: Given the sum of the first $n$ terms of the sequence $(a_n)$ as $$S_n = n^2 + 2n$$ for each natural number $n \geq 1$, find the third term $a_3$ of the sequence. 2. Recall the formula for the $n$-th term of a sequence from its partial sums: $$a_n = S_n - S_{n-1}$$ where $S_0 = 0$. 3. Calculate $a_3$ using the formula: $$a_3 = S_3 - S_2$$ 4. Compute $S_3$ and $S_2$: $$S_3 = 3^2 + 2 \times 3 = 9 + 6 = 15$$ $$S_2 = 2^2 + 2 \times 2 = 4 + 4 = 8$$ 5. Substitute values: $$a_3 = 15 - 8 = 7$$ 6. Therefore, the third term of the sequence is $7$. Answer: B. 7