Question

NO LINKS!! Please help me with this problem. Part 4ff​

Answer 1

-12150

Explanation:

Given series:

`\displaystyle \sum^(100)_(n=1) \left(-3n+30\right)`

The series is arithmetic.

Calculate the first and last terms:

`\begin{aligned}\implies a_1&=-3(1)+30\\&=-3+30\\&=27\end{aligned}`

`\begin{aligned}\implies a_(100)&=-3(100)+30\\&=-300+30\\&=-270\end{aligned}`

`\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=(n)/(2)(a_1+a_n)$\\\\where:\\\phantom{ww}$\bullet$ $a_1$ is the first term. \\ \phantom{ww}$\bullet$ $a_n$ is the last term.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}`

Substitute n = 100, a₁ = 27 and aₙ = 270 into the formula and solve:

`\implies S_(100)=(100)/(2)\left(27-270\right)`

`\implies S_(100)=50\left(-243\right)`

`\implies S_(100)=-12150`