1. **State the problem:** Find the sum of the first 20 terms of an arithmetic progression (AP) where the first term $a_1=7$ and the common difference $d=3$. 2. **Formula used:** The sum of the first $n$ terms of an AP is given by $$S_n = \frac{n}{2} \times (2a_1 + (n-1)d)$$ where $S_n$ is the sum, $a_1$ is the first term, $d$ is the common difference, and $n$ is the number of terms. 3. **Apply the values:** Here, $n=20$, $a_1=7$, and $d=3$. 4. **Calculate inside the parentheses:** $$2a_1 + (n-1)d = 2 \times 7 + (20-1) \times 3 = 14 + 19 \times 3 = 14 + 57 = 71$$ 5. **Calculate the sum:** $$S_{20} = \frac{20}{2} \times 71 = 10 \times 71 = 710$$ 6. **Final answer:** The sum of the first 20 terms is **710**.