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An arithmetic series is a series whose related sequence is arithmetic. It results from adding the terms of an arithmetic sequence .
Example 1:
Finite arithmetic sequence:
Related finite arithmetic series:
Written in sigma notation:
Example 2:
Infinite arithmetic sequence:
Related infinite arithmetic series:
Written in sigma notation:
To find the sum of the first
terms of an arithmetic sequence, use the formula
,
where
is the number of terms,
is the first term, and
is the last term.
Example 3:
Find the sum of the first 20 terms of the arithmetic series if and .
Example 4:
Find the sum of the first
terms of the arithmetic series
.
First find the term:
Then find the sum:
Example 5:
Find the sum:
First find and :
Then find the sum: