Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
-$$\sum _ { i = 1 } ^ { 39 } ( - 2 i - 1 )$$
A) $- 1599$
B) $- 1560$
C) $- 1404$
D) $- 1267.5$

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 $n$ is the number of terms, $a$ is the first term, and $d$ is the common difference. Here, $a = -2(1) - 1 = -3$, $d = -2$, and $n = 39$. Plugging these values into the formula gives $S_{39} = \frac{39}{2} [2(-3) + (39 - 1)(-2)] = \frac{39}{2} [-6 - 76] = \frac{39}{2} [-82] = -1599$.

Use the Formula for the Sum of the First N ∑i=139(−2i−1)\sum _ { i = 1 } ^ { 39 } ( - 2 i - 1 )i=1∑39​(−2i−1)

Use the Formula for the Sum of the First N $\sum _ { i = 1 } ^ { 39 } ( - 2 i - 1 )$