Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence
-Find 2 + 4 + 6 + 8 + . . ., the sum of the first 40 positive even integers.
A)1640
B)1644
C)1599
D)1595

Question

Quizplus · Accepted Answer

The sum of the first n terms of an arithmetic sequence can be found using the formula $S_n = \frac{n}{2}(a_1 + a_n)$, where $S_n$ is the sum of the first n terms, $a_1$ is the first term, $a_n$ is the nth term, and n is the number of terms. For the first 40 positive even integers, $a_1 = 2$, $a_n = 80$ (since the nth term, where n=40, is 2n = 80), and $n = 40$. Plugging these values into the formula gives $S_{40} = \frac{40}{2}(2 + 80) = 20 \times 82 = 1640$.

Use the Formula for the Sum of the First N