Suggested languages for you:

Americas

Europe

Q 74.

Expert-verified
Found in: Page 809

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# In Problems 71-82, find the sum of each sequence.$\underset{k=1}{\overset{24}{\sum \left(-}}k\right)$

The sum of this sequence is (-300).

See the step by step solution

## Step 1. Write the given information.

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

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

The formula for summation is:$\underset{k=1}{\overset{n}{\sum k}}=1+2+...+n\phantom{\rule{0ex}{0ex}}⇒\underset{k=1}{\overset{n}{\sum k}}=\frac{n\left(n+1\right)}{2}\phantom{\rule{0ex}{0ex}}$

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

Using the formula gives:

$\underset{k=1}{\overset{24}{\sum \left(-k\right)}}=\underset{k=1}{\overset{24}{-\sum \left(k\right)}}\phantom{\rule{0ex}{0ex}}⇒\underset{k=1}{\overset{24}{-\sum \left(k\right)}}=-\frac{24×\left(24+1\right)}{2}\phantom{\rule{0ex}{0ex}}⇒\underset{k=1}{\overset{24}{-\sum k}}=-\frac{24×\left(25\right)}{2}\phantom{\rule{0ex}{0ex}}⇒\underset{k=1}{\overset{24}{-\sum k}}=-300\phantom{\rule{0ex}{0ex}}$