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.
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
Find the sum of the first 60 terms of the arithmetic sequence
We should first find the 60 th term:
Therefore we use the formula,
Then to find the sum:
S60=60(3 + 121)/2= 3720