Sum of the First Terms of an Arithmetic Sequence
Suppose a sequence of numbers is arithmetic (that is, it increases or decreases by a constant amount each term), and you want to find the sum of the first terms.
Denote this partial sum by . Then
,
where
is the number of terms,
is the first term and
is the last term.
The sum of the first terms of an arithmetic sequence is called an arithmetic series .
Example 1:
Find the sum of the first terms of the arithmetic series if and .
Example 2:
Find the sum of the first terms of the arithmetic sequence .
First find the term:
Then find the sum:
Example 3:
Find the sum:
First find and :
Then find the sum:
See also: sigma notation of a series and nth term of an arithmetic sequence