Find the sum of the arithmetic series. $$\sum _ { i = 1 } ^ { 18 } ( - 5 i - 8 )$$
A) $- 999$
B) $- 53$
C) $- 49$
D) $- 882$

Question

Quizplus · Accepted Answer

The given series is an arithmetic series where each term is given by the formula $a_i = -5i - 8$, with $i$ ranging from 1 to 18. To find the sum of this series, we can use the formula for the sum of an arithmetic series, $S_n = \frac{n}{2}(a_1 + a_n)$, where $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the last term. First, find the first term $a_1$ by substituting $i = 1$:$$a_1 = -5(1) - 8 = -5 - 8 = -13$$Then, find the last term $a_{18}$ by substituting $i = 18$:$$a_{18} = -5(18) - 8 = -90 - 8 = -98$$Now, use the sum formula:$$S_{18} = \frac{18}{2}(-13 - 98) = 9 \times (-111) = -999$$Therefore, the sum of the series is $-999$.

Find the Sum of the Arithmetic Series ∑i=118(−5i−8)\sum _ { i = 1 } ^ { 18 } ( - 5 i - 8 )i=1∑18​(−5i−8)

Find the Sum of the Arithmetic Series $\sum _ { i = 1 } ^ { 18 } ( - 5 i - 8 )$