Find the sum of the arithmetic sequence.
-2 + 4 + 6 + ... + 678
A) 115,260
B) 114,582
C) 115,600
D) 114,921

Question

Quizplus · Accepted Answer

The sum 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. Here, $a_1 = 2$, $a_n = 678$, and the common difference $d = 2$. To find $n$, we use the formula for the nth term of an arithmetic sequence: $a_n = a_1 + (n - 1)d$. Substituting the given values, we get $678 = 2 + (n - 1)2$, which simplifies to $676 = 2(n - 1)$, so $n = 339$. Substituting $n$, $a_1$, and $a_n$ into the sum formula gives $S_n = \frac{339}{2}(2 + 678) = 169.5 \times 680 = 115,260$.

Find the Sum of the Arithmetic Sequence