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Arithmetic Series
Anarithmetic series是一个serieswhose relatedsequence是一个rithmetic. It results from adding thetermsof anarithmetic 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:
找到th的总和e firstterms of an arithmetic sequence, use the formula
,
whereis the number of terms,is the first term, andis the last term.
Example 3:
Find the sum of the first 20 terms of the arithmetic series ifand.
Example 4:
Find the sum of the firstterms of the arithmetic series
.
First find theterm:
Then find the sum:
Example 5:
Find the sum:
First findand:
Then find the sum: