Sum of the First n Terms of an Arithmetic Sequence
If a sequence is arithmetic the sum of the first n terms, denoted Sn, there are ways to find its sum without actually adding all of the terms.
To find the sum of the first n terms of an arithmetic sequence use the formula,
,
where n is the number of terms, a1 is the first term and an is the last term.
The sum of the first n terms of a arithmetic sequence is called arithmetic series.
Example 1:
Find the sum of the first 20 terms of the arithmetic series if a1 = 5 and a20 = 62.
Example 2:
Find the sum of the first 40 terms of the arithmetic sequence 2, 5, 8, 11, ···.
First find the 40th term:
Then find the sum:
Example 3:
Find the sum:
First find a1 and a50:
a1 = 3(1) + 2 = 5
a50 = 3(50) + 2 = 152
Then find the sum:
