The sum of the first $10$ terms of the arithmetic progression $2,5,8,11,\dots$ is

Solution

1. Identify the first term $a=2$, common difference $d=3$, and number of terms $n=10$.
2. Use the sum formula $S_n=\frac{n}{2}[2a+(n-1)d]$.
3. Substitute the values: $S_{10}=\frac{10}{2}[2(2)+(10-1)3]$.
4. Calculate $$\begin{array}{rl}{S}_{10}& =5[4+27]\\ & =5\times 31\\ & =155\end{array}$$.
5. Hence the answer is (A).