Sum Of The First nn  Terms Of An Arithmetic Series

 

If a series is arithmetic, the sum of the first n terms of the series is denoted as Sn .

The sum can be found without adding all of the terms by using the following  formula

Sn=n(a1 + an) / 2

 where n is the number of terms, a1 is the first term and an is the last term. 

Example 1:

Find the sum of the first 10 terms of the arithmetic series if a1=3 and a10=54 .

S10=10(3 + 54)/2

S10=570/2 = 285

Example 2:

Find the sum of the first 60 terms of the arithmetic sequence 

3,5,7,9,11⋯ 

We should first find the 60 th term:

Therefore we use the formula,

A60=a1+(n−1)d       

=3+59(2)=121

Then to find the sum:

Sn=n(a1+an)/2

S60=60(3 + 121)/2= 3720