Chapter 8, Problem 41RE

To determine

To find the sum of the first $50$ positive multiples of $5$ .

Answer to Problem 41RE

Thesum is $6375$ .

Explanation of Solution

Given: First $50$ positive multiples of $5$ .

Formula Used:

Sum of an Arithmetic Sequence: $S_n=\frac{n}{2}\left[a+l\right]$ ; where $a$ is the first term and $l$ is the last term.

Calculation:

Given:Sum offirst $50$ positive multiples of $5$ is given as:

  $5+10+15+20+\mathrm{....}+250$

Using the above formula, we have:

  $S_n=\frac{n}{2}\left[a+l\right]$

  $\begin{array}{l}{S}_{50}=\frac{50}{2}\left[5+250\right]\\ S_{50}=6375\end{array}$

Sum is $6375$ .

Conclusion:

Hence, the sum is $6375$ .