Question

Find $S_n$for each arithmetic series described.

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

Short answer

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

Step-by-step solution

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 $S_{20}=230$.