Question

Partial Sums of an Arithmetic Sequence Find the partial sum $S_n$ of the arithmetic sequence that satisfies the given conditions.

$a=3,d=5,n=20$

Short answer

The required partial sum is $1010$.

Step-by-step solution

Step 1. Given information.

The given conditions are:

$\begin{array}{l}a=3\\ d=5\\ n=20\end{array}$

Step 2. Write the concept.

The partial sum of $n$ term of an arithmetic sequence is:

$S_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right]$

Where $a$ is the first term and $d$ is a common difference.

Step 3. Determine the partial sum.

Substitute $a=3,d=5,n=20$in the above formula to find the partial sum.

$\begin{array}{c}{S}_{20}=\frac{20}{2}\left[2\left(3\right)+\left(20-1\right)5\right]\\ =10\left[6+\left(19\right)5\right]\\ =10\left[6+95\right]\\ =10\left[101\right]\\ =1010\end{array}$

Thus, the required partial sum is $1010$.