Question

Find the sum
Algebra 2 Grade 11

Answer 1

-33

Explanation:

Sigma notation is a mathematical notation used to represent the sum of a series of terms. It provides a concise way to express the total of a sequence of numbers or mathematical expressions.

Sigma notation

`\large\boxed{\displaystyle \sum^(k)_(n=b)a_n}`

where:

• n is the summation index.
• b is the first value of n.
• k is the last value of n.
• aₙ is the formula for each term.

Given sigma notation:

`\displaystyle \sum^(15)_(n=8)\left((n)/(4)-7\right)`

Therefore:

• n is the summation index.
• n = 8 is the first value of n.
• n = 15 is the last value of n.
• (n/4 - 7) is the formula for the terms.

To calculate the sum of the given sigma notation, we can substitute the values of n from 8 to 15 into the term formula and add them up:

`\begin{aligned}\displaystyle \sum^(15)_(n=8)\left((n)/(4)-7\right)&=\left((8)/(4)-7\right)+\left((9)/(4)-7\right)+\left((10)/(4)-7\right)+\left((11)/(4)-7\right)+\left((12)/(4)-7\right)\\&\;\;\;\;\;+\left((13)/(4)-7\right)+\left((14)/(4)-7\right)+\left((15)/(4)-7\right)\end{aligned}`

There are 8 terms. Each term subtracts 7 from the fraction n/4.

Therefore:

`\begin{aligned}\displaystyle \sum^(15)_(n=8)\left((n)/(4)-7\right)&=\left((8)/(4)+(9)/(4)+(10)/(4)+(11)/(4)+(12)/(4)+(13)/(4)+(14)/(4)+(15)/(4)\right)-7 \cdot 8\\\\&=(92)/(4)-56\\\\&=23-56\\\\&=-33\end{aligned}`

So, the sum is:

`\large\boxed{\boxed{-33}}`