Find the sum of the arithmetic sequence.
-6 + 12 + 18 + ... + 876
A) 64827
B) 64386
C) 63510
D) 63948

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, $a_1 = 6$, $a_n = 876$, and the common difference $d = 6$. 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, $876 = 6 + (n - 1)6$, solving for $n$ gives $n = 146$. Substituting $n$, $a_1$, and $a_n$ into the sum formula gives $S_n = \frac{146}{2}(6 + 876) = 73 \times 882 = 64386$.

Find the Sum of the Arithmetic Sequence