Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
-$\sum _ { \mathrm { i } = 1 } ^ { 90 } - 4 \mathrm { i }$
A) $- 16,380$
B) $- 16,562$
C) $- 16,198$
D) $- 16,376$

Question

Quizplus · Accepted Answer

The sum of the first n terms of an arithmetic sequence is given by $S_n = \frac{n}{2} [2a + (n - 1)d]$, where $n$ is the number of terms, $a$ is the first term, and $d$ is the common difference. In this case, $n = 90$, $a = -4$ (since the first term when i=1 is $-4 \times 1 = -4$), and $d = -4$ (since each term decreases by 4). Plugging these values into the formula gives $S_{90} = \frac{90}{2} [2(-4) + (90 - 1)(-4)] = 45[-8 - 356] = 45 \times -364 = -16,380$.

Use the Formula for the Sum of the First N ∑i=190−4i\sum _ { \mathrm { i } = 1 } ^ { 90 } - 4 \mathrm { i }∑i=190​−4i

Use the Formula for the Sum of the First N $\sum _ { \mathrm { i } = 1 } ^ { 90 } - 4 \mathrm { i }$