Question

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

$a=10,d=-8,n=30$

Short answer

The required partial sum is $-3180$.

Step-by-step solution

Step 1. Given information.

The given conditions are:

$\begin{array}{l}a=10\\ d=-8\\ n=30\end{array}$

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 $a=10,d=-8,n=30$in the above formula to find the partial sum.

$\begin{array}{c}{S}_{30}=\frac{30}{2}\left[2\left(10\right)+\left(30-1\right)\left(-8\right)\right]\\ =15\left[20-8\left(29\right)\right]\\ =15\left[20-232\right]\\ =15\left[-212\right]\\ =-3180\end{array}$

Thus, the required partial sum is $-3180$.