## Arithmetic Series

If terms of an arithmetic sequence are added together an arithmetic series is formed.

2 + 4 + 6 + 8 is a finite arithmetic series
2 + 4 + 6 + 8 + ... is an infinte arithmetic series

To find the sum of the first n terms of an arithmetic sequence use the formula:

 Sum of first n terms of arithmetic sequence d = common differencea = first termn = number of terms

OR

An equivalent formula involving the last term, l

 Sum of first n terms of arithmetic sequence

Example 1

What is the sum of the first 15 terms of the arithmetic sequence:

3, 6, 9, 12, ...

 Common difference d = 3 Number of terms n = 15 First term a = 3

Example 2

The first term of an arithmetic sequence is 5 and the last term is 250.

The sum of this series is 1020.

How many terms does it have?

 First term a = 5 Last term l = 250 Sum of n terms Sn = 1020

Example 3

An athlete does 20 press-ups on the first day of a training routine. On the second day she does 24 press-ups and on the third day 28 press-ups.

If she follows this pattern for 30 days, how many press-up will she have done altogether?

 First term a = 20 Common difference d = 4 Number of terms n = 30