# Arithmetic series

### Arithmetic series

An arithmetic series is the sum of an arithmetic sequence. In this lesson, we will learn how to solve problems using the arithmetic series formula.
Basic concepts: Arithmetic sequences,

#### Lessons

• the sum of $n$ terms of an arithmetic series:
${s_n}$= $\frac{n}{2}[2{t_1} + (n - 1)d]$
= $\frac{n}{2}[{t_1} + {t_n}]$
• 1.
Arithmetic series formula
Determine the sum of the first ten terms of the arithmetic series: 6 + 1 – 4 – 9 – … .

• 2.
Problem involving both arithmetic sequence formula and arithmetic series formula
Find the sum of the arithmetic series: – 4 – 1 + 2 + …. + 329.

• 3.
$t_{n}=s_{n}-s_{n-1}$
The sum of the first n terms of an arithmetic series is ${s_n} = 7{n^2} - 5n$ .
a)
Find the common difference.

b)
Determine the first six terms of the corresponding arithmetic sequence.

• 4.
A triangle has a perimeter of 32m; the shortest side is 6 m long. If the side lengths of this triangle form an arithmetic sequence, what are the other side lengths?