Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence
-Find the sum of the first 42 terms of the arithmetic sequence: 2, 4, 6, 8, . . .
A) 1806
B) 1816
C) 86
D) 1848

Question

Quizplus · Accepted Answer

The formula for the sum of the first n terms of an arithmetic sequence is $S_n = \frac{n}{2}(a_1 + a_n)$, 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. Here, $a_1 = 2$, $n = 42$, and the common difference $d = 2$. The nth term $a_n = a_1 + (n-1)d = 2 + (42-1) \times 2 = 2 + 82 = 84$. Thus, $S_n = \frac{42}{2}(2 + 84) = 21 \times 86 = 1806$.

Use the Formula for the Sum of the First N