Question

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

Answer 1

The common difference for this arithmetic sequence is $12-5 = 7$. The first term is 5 and the last term is $5 + 7 \cdot 199 = 5 + 1393 = 1398$. The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms, so the sum of the first 200 terms is $\frac{5+1398}{2} \cdot 200 = \boxed{280,600}$.