Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
-$$\sum _ { i = 1 } ^ { 31 } ( - 4 i - 8 )$$
A) $- 2092.5$
B) $- 2170$
C) $- 2232$
D) $- 1984$

Question

Quizplus · Accepted Answer

The sum of the first $n$ terms of an arithmetic sequence can be found using the formula $S_n = \frac{n}{2} [2a + (n - 1)d]$, where $S_n$ is the sum of the first $n$ terms, $a$ is the first term, $d$ is the common difference, and $n$ is the number of terms. For the given sequence, the first term $a = -4(1) - 8 = -12$, the common difference $d = -4$, and $n = 31$. Plugging these values into the formula gives $S_{31} = \frac{31}{2} [2(-12) + (31 - 1)(-4)] = \frac{31}{2} [-24 - 120] = \frac{31}{2} [-144] = -2232$.

Use the Formula for the Sum of the First N ∑i=131(−4i−8)\sum _ { i = 1 } ^ { 31 } ( - 4 i - 8 )i=1∑31​(−4i−8)

Use the Formula for the Sum of the First N $\sum _ { i = 1 } ^ { 31 } ( - 4 i - 8 )$