Question

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

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

Short answer

The sum of this sequence is (-300).

Step-by-step solution

Step 1. Write the given information. 

The sum of sequence:$\underset{k=1}{\overset{24}{\sum (-}}k)$.

Step 2. Use the formula for sum of sequence of n real numbers. 

The formula for summation is:
$$\begin{gathered} \underset{k=1}{\overset{n}{\sum k}}=1+2+...+n \\ \Rightarrow \underset{k=1}{\overset{n}{\sum k}}=\frac{n(n+1)}{2} \end{gathered}$$

Step 3. Use the formula with c = (-k) and n=24.

Using the formula gives:

$$\begin{gathered} \underset{k=1}{\overset{24}{\sum (-k)}}=\underset{k=1}{\overset{24}{-\sum \left(k\right)}} \\ \Rightarrow \underset{k=1}{\overset{24}{-\sum \left(k\right)}}=-\frac{24\times (24+1)}{2} \\ \Rightarrow \underset{k=1}{\overset{24}{-\sum k}}=-\frac{24\times \left(25\right)}{2} \\ \Rightarrow \underset{k=1}{\overset{24}{-\sum k}}=-300 \end{gathered}$$