Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
-$$\sum _ { i = 1 } ^ { 44 } ( - 3 i - 7 )$$
A) $- 3278$
B) $- 3212$
C) $- 3102$
D) $- 2948$

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, $n$ is the number of terms, and $d$ is the common difference. For the given sequence, the first term $a$ can be found by substituting $i = 1$ into the given formula, yielding $a = -3(1) - 7 = -10$. The common difference $d$ is the coefficient of $i$, which is $-3$. Substituting $n = 44$, $a = -10$, and $d = -3$ into the sum formula gives $S_{44} = \frac{44}{2} [2(-10) + (44 - 1)(-3)] = 22[-20 - 129] = 22[-149] = -3278$.

Use the Formula for the Sum of the First N ∑i=144(−3i−7)\sum _ { i = 1 } ^ { 44 } ( - 3 i - 7 )i=1∑44​(−3i−7)

Use the Formula for the Sum of the First N $\sum _ { i = 1 } ^ { 44 } ( - 3 i - 7 )$