Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
-$$\sum _ { i = 1 } ^ { 44 } ( 5 i - 3 )$$
A) 4818
B) 4708
C) 4928
D) 5082

Question

Quizplus · Accepted Answer

The given sum is an arithmetic series where each term can be represented as $a_i = 5i - 3$. The first term $a_1 = 5(1) - 3 = 2$, and the common difference $d = 5$, since each term increases by 5. The sum of the first $n$ terms of an arithmetic series is given by $S_n = \frac{n}{2} [2a_1 + (n - 1)d]$. Substituting $n = 44$, $a_1 = 2$, and $d = 5$, we get $S_{44} = \frac{44}{2} [2(2) + (44 - 1)5] = 22 [4 + 215] = 22 \times 219 = 4818$.

Use the Formula for the Sum of the First N ∑i=144(5i−3)\sum _ { i = 1 } ^ { 44 } ( 5 i - 3 )i=1∑44​(5i−3)

Use the Formula for the Sum of the First N $\sum _ { i = 1 } ^ { 44 } ( 5 i - 3 )$