Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
-$\sum _ { i = 1 } ^ { 25 } ( - 5 i - 3 )$
A) -1700
B) -1525
C) -1612.5
D) -1637.5

Question

Quizplus · Accepted Answer

The given sum can be simplified as an arithmetic series where the first term $a_1 = -5(1) - 3 = -8$ and the common difference $d = -5$. The sum of the first $n$ terms of an arithmetic sequence is given by $S_n = \frac{n}{2}[2a_1 + (n-1)d]$. Substituting $n = 25$, $a_1 = -8$, and $d = -5$, we get $S_{25} = \frac{25}{2}[2(-8) + (25-1)(-5)] = \frac{25}{2}[-16 - 120] = \frac{25}{2} \times -136 = -1700$.

Use the Formula for the Sum of the First N ∑i=125(−5i−3)\sum _ { i = 1 } ^ { 25 } ( - 5 i - 3 )∑i=125​(−5i−3)

Use the Formula for the Sum of the First N $\sum _ { i = 1 } ^ { 25 } ( - 5 i - 3 )$