Question

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

$a_1=55,d=12,n=10$

Short answer

The required partial sum is $1090$.

Step-by-step solution

Step 1. Given information.

The given conditions are:

$\begin{array}{l}{a}_1=55\\ d=12\\ n=10\end{array}$

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 $a=55,d=12,n=10$in the above formula to find the partial sum.

$\begin{array}{c}{S}_{10}=\frac{10}{2}\left[2\left(55\right)+\left(10-1\right)\left(12\right)\right]\\ =5\left[110+\left(9\right)\left(12\right)\right]\\ =5\left[110+108\right]\\ =5\left[218\right]\\ =1090\end{array}$

Thus, the required partial sum is $1090$.