Use the partial sum formula to find the partial sum of the given arithmetic sequence.
-Find the sum of the first four terms of the arithmetic sequence: -3, -15, -27, . . . .
A) 84
B) -60
C) - 84
D) -45

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, and $a_n$ is the nth term. Here, $n = 4$, $a_1 = -3$, and the common difference $d = -12$. The fourth term $a_4 = a_1 + 3d = -3 + 3(-12) = -3 - 36 = -39$. Thus, $S_4 = \frac{4}{2}(-3 - 39) = 2(-42) = -84$.

Use the Partial Sum Formula to Find the Partial Sum