Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
-$$\sum _ { \mathrm { i } = 1 } ^ { 27 } ( 2 \mathrm { i } - 5 )$$
A) 621
B) 594
C) 729
D) $823.5$

Question

Quizplus · Accepted Answer

The sum 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. Here, $a = 2(1) - 5 = -3$, $d = 2$, and $n = 27$. Plugging these values into the formula gives $S_{27} = \frac{27}{2} [2(-3) + (27 - 1)2] = \frac{27}{2} [-6 + 52] = \frac{27}{2} \times 46 = 621$.

Use the Formula for the Sum of the First N ∑i=127(2i−5)\sum _ { \mathrm { i } = 1 } ^ { 27 } ( 2 \mathrm { i } - 5 )i=1∑27​(2i−5)

Use the Formula for the Sum of the First N $\sum _ { \mathrm { i } = 1 } ^ { 27 } ( 2 \mathrm { i } - 5 )$