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 difference
a = first term
n = number of terms

Y11_Arithmetic_Series_01.gif

OR

An equivalent formula involving the last term, l

Sum of first n terms of arithmetic sequence
Y11_Arithmetic_Series_02.gif

 

 

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

Y11_Arithmetic_Series_03.gif

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

Y11_Arithmetic_Series_04.gif

 

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

Y11_Arithmetic_Series_05.gif