Q4. - Algebra 2

Question

Find $S_n$  for each arithmetic series described.

$a_1=4,a_n=100,n=25$

Step-by-Step Solution

Answer

$S_n$  for the arithmetic series is $S_{25}=1300$ .

Step 1. Given Information.

Given arithmetic series is $a_1=4,a_n=100,n=25$ .

Step 2. Calculation .

The sum $S_n$  of the first n terms of an arithmetic series is given by   

 $S_n=\frac{n}{2}(a_1+a_n)$

Here,  $a_1=4,a_n=100,n=25$

Plugging the values:

$\begin{array}{l}{S}_n=\frac{n}{2}(a_1+a_n)\\ S_{25}=\frac{25}{2}(4+100)\\ S_{25}=\frac{25}{2}\left(104\right)\\ S_{25}=25\left(52\right)\\ S_{25}=1300\end{array}$

Step 3. Conclusion .

Hence, the sum is $S_{25}=1300$ .