Q5. - Algebra 2

Question

Find  $S_n$ for each arithmetic series described.

$a_1=40,n=20,d=-3$

Step-by-Step Solution

Answer

 $S_n$ for the arithmetic series is $S_{20}=230$ .

Step 1. Given Information.

Given arithmetic series is $a_1=40,n=20,d=-3$ .

Step 2. Calculation .

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

 $S_n=\frac{n}{2}(2a_1+(n-1)d)$

Here,  $a_1=40,n=20,d=-3$

Plugging the values:

$\begin{array}{l}{S}_n=\frac{n}{2}(2a_1+(n-1)d)\\ S_{20}=\frac{20}{2}(2\left(40\right)+(20-1)(-3))\\ S_{20}=10(80+\left(19\right)(-3))\\ S_{20}=10(80-57)\\ S_{20}=10\left(23\right)\\ S_{20}=230\end{array}$

Step 3. Conclusion .

Hence, the sum is $S_{20}=230$ .