Ch.9 Sequences and Series
Section 4 –Arithmetic Series
Definitions:
Series: the sum of the terms of a
sequence.
Finite Series: has a first and last
term.
Infinite Series: Continues without
end.
EXample
Finite Sequence
6,9,12,15,18
Infinite Sequence
3,7,11,15,…
Finite Series
6+9+12+15+18=(60)
Infinite Series
3+7+11+15+…
Definition: Arithmetic
Series
A series whose terms form an
arithmetic sequence.
Sum of a Finite Arithmetic Series
𝑎1 + 𝑎2 + 𝑎3 + ⋯ + 𝑎𝑛
𝑛
(𝑎1 +𝑎𝑛 )
2
𝑆𝑛 =
Where 𝑎1 is the
first term and 𝑎𝑛 is the nth term.
EXample
What is the sum of the even
integers from 2 to 100?
EXample
A company pays a bonus to
salespeople at the end of their
first 50 weeks if they make 10
sales in their first week and, then
improve their sales by two each
week thereafter. How many sales
would someone need to get the
bonus?