Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
-$\sum _ { i = 1 } ^ { 25 } ( 2 i - 7 )$
A) 587.5
B) 475
C) 675
D) 450

Question

Quizplus · Accepted Answer

The sum of an arithmetic sequence can be found using the formula $S_n = \frac{n}{2}(a_1 + a_n)$, where $S_n$ is the sum of the first $n$ terms, $a_1$ is the first term, $a_n$ is the nth term, and $n$ is the number of terms. For the given sequence, $a_1 = 2(1) - 7 = -5$, $a_{25} = 2(25) - 7 = 43$, and $n = 25$. Plugging these values into the formula gives $S_{25} = \frac{25}{2}(-5 + 43) = \frac{25}{2}(38) = 475$.

Use the Formula for the Sum of the First N ∑i=125(2i−7)\sum _ { i = 1 } ^ { 25 } ( 2 i - 7 )∑i=125​(2i−7)

Use the Formula for the Sum of the First N $\sum _ { i = 1 } ^ { 25 } ( 2 i - 7 )$