Question

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

$\sum _{k=1}^{40}8$

Short answer

The sum of this sequence is 400.

Step-by-step solution

Step 1. Write the given information.

The sum of sequence:

$\sum _{k=1}^{50}8;k=1,...,50$

Step 2. Use the formula for sum of sequence. 

The formula for summation is:

$$\begin{gathered} \underset{k=1}{\overset{n}{\sum c}}=c+c+...+c \\ \Rightarrow \underset{k=1}{\overset{n}{\sum c}}=cn,c-realnumber \end{gathered}$$

Step 3. Use the formula with c=8 and n=50.

Using the formula gives:

$$\begin{gathered} \underset{k=1}{\overset{50}{\sum 8}}=8+8+...+8 \\ \Rightarrow \underset{k=1}{\overset{50}{\sum 8}}=50\times 8 \\ \Rightarrow \underset{k=1}{\overset{50}{\sum 8}}=400 \end{gathered}$$