Solve the problem.
-The finite sequence whose general term is $$a _ { n } = 0.16 n ^ { 2 } - 1.06 n + 7.25$$
where $\mathrm { n } = 1,2,3 , \ldots , 9$ models the total operating costs, in millions of dollars, for a company from 1991 through $1999 .$
Find $\sum _ { i = 1 } ^ { 5 } a _ { i }$
A) $\$ 29.15$ million
B) $\$ 31.75$ million
C) $\$ 23.2$ million
D) $\$ 25.4$ million

Question

Quizplus · Accepted Answer

To find $\sum _ { i = 1 } ^ { 5 } a _ { i }$, we substitute $i = 1, 2, 3, 4, 5$ into the given formula $a _ { n } = 0.16 n ^ { 2 } - 1.06 n + 7.25$ and sum the results:- For $i = 1$: $0.16(1)^2 - 1.06(1) + 7.25 = 0.16 - 1.06 + 7.25 = 6.35$- For $i = 2$: $0.16(2)^2 - 1.06(2) + 7.25 = 0.64 - 2.12 + 7.25 = 5.77$- For $i = 3$: $0.16(3)^2 - 1.06(3) + 7.25 = 1.44 - 3.18 + 7.25 = 5.51$- For $i = 4$: $0.16(4)^2 - 1.06(4) + 7.25 = 2.56 - 4.24 + 7.25 = 5.57$- For $i = 5$: $0.16(5)^2 - 1.06(5) + 7.25 = 4.00 - 5.30 + 7.25 = 5.95$Summing these values: $6.35 + 5.77 + 5.51 + 5.57 + 5.95 = 29.15$.

Solve the Problem an=0.16n2−1.06n+7.25a _ { n } = 0.16 n ^ { 2 } - 1.06 n + 7.25an​=0.16n2−1.06n+7.25

Solve the Problem $a _ { n } = 0.16 n ^ { 2 } - 1.06 n + 7.25$