Find the sum of the first $20$ terms of an arithmetic progression whose first term is $a=5$ and common difference is $d=3$.

Solution

1. The sum of the first $n$ terms is given by $S_n=\frac{n}{2}[2a+(n-1)d]$.
2. Substitute $n=20$, $a=5$, and $d=3$ into the formula.
3. $$\begin{array}{rl}{S}_{20}& =\frac{20}{2}[2(5)+(20-1)3]\\ & =10[10+57]\\ & =10(67)\\ & =670\end{array}$$.
4. Hence the answer is (A).