Chapter 12.1, Problem 74AYU

In Problems 71-82, find the sum of each sequence.

${\displaystyle \underset{k=1}{\overset{24}{\sum }}\left(-k\right)}$

To determine

To find: The sum of given sequence: ${\displaystyle \sum }_{k=1}^{24}\left(-k\right)$.

Answer to Problem 74AYU

${\displaystyle \sum }_{k=1}^{24}\left(-k\right)=-300$

Explanation of Solution

Given:

${\displaystyle \sum }_{k=1}^{24}\left(-k\right)$

Calculation:

Using ${\displaystyle \sum }_{\text{k }=1}^{\text{n}}k=1+2+3+\dots +\text{ n }=\frac{n\left(n+1\right)}{2}$ we have

${\displaystyle \sum }_{k=1}^{24}\left(-k\right)=-\left(1+2+3+\dots +24\right)=-\left[\frac{24\left(24+1\right)}{2}\right]=-300$