Question

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

$a=-2,d=23,n=25$

Short answer

The required partial sum is $6850$.

Step-by-step solution

Step 1. Given information.

The given conditions are:

$\begin{array}{l}a=-2\\ d=23\\ n=25\end{array}$

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 $a=-2,d=23,n=25$in the above formula to find the partial sum.

$\begin{array}{c}{S}_{25}=\frac{25}{2}\left[2\left(-2\right)+\left(25-1\right)\left(23\right)\right]\\ =\frac{25}{2}\left[-4+\left(24\right)\left(23\right)\right]\\ =\frac{25}{2}\left[-4+552\right]\\ =\frac{25}{2}\left[548\right]\\ =25\left(274\right)\\ =6850\end{array}$

Thus, the required partial sum is $6850$.