Question

What is the sum of the first 200 terms of the arithmetic sequence 5, 12, 19,
26, ...?

Answer 1

We see that the common difference is $12-5=19-12=26-19=\cdots=7$. Looking at the first few terms, we see that the $n$th term is $5 + 7(n - 1)$, so the 200th term is $5 + 7(200 - 1) = 1403$. Using the arithmetic series formula, the sum of the first 200 terms is
\[\frac{200}{2}(5 + 1403) = \frac{200 \cdot 1408}{2} = \boxed{140{,}800}.\]