Find the indicated sum.
-$$\sum _ { n = 1 } ^ { 37 } ( 2 n - 4 )$$
A) 1258
B) 1221
C) 1480
D) $1350.5$

Question

Quizplus · Accepted Answer

The sum can be simplified by distributing the summation: $\sum _ { n = 1 } ^ { 37 } 2n - \sum _ { n = 1 } ^ { 37 } 4$. The first part is an arithmetic series with a common difference of 2, and the second part is a constant multiplied by the number of terms. The sum of the first part is $2 \times \frac{37(37 + 1)}{2} = 37 \times 38$, and the sum of the second part is $37 \times 4$. Simplifying gives $37 \times 38 - 37 \times 4 = 37 \times (38 - 4) = 37 \times 34 = 1258$.

Find the Indicated Sum ∑n=137(2n−4)\sum _ { n = 1 } ^ { 37 } ( 2 n - 4 )n=1∑37​(2n−4)

Find the Indicated Sum $\sum _ { n = 1 } ^ { 37 } ( 2 n - 4 )$