Arithmetic Series

1. Homework Questions

2. Arithmetic Series
Mrs. Ramsey

3. Arithmetic Series
A series is the expression for the SUM of
the terms in a sequence.
Finite sequences and series have terms
you can count individually from 1 to a
final whole number, n.
Infinite sequences and series continue
without end. (infinity)

4. Examples
 Finite Sequence:
 6, 9, 12, 15, 18
 Finite Series:
 6 + 9 + 12 + 15+ 18
 Infinite Sequence:
 3, 7, 11, 15…
 Infinite Series:
 3 + 7 + 11 + 15 +…

5. Finite Sequence
2, 11, 20, 29, 38, 47
Write the related series:
Evaluate the series:

6. An arithmetic series is a series whose
terms form an arithmetic sequence.
Sum of a Finite Arithmetic Series:

a1: 1st
term
an: nth term
n: number of terms
)(
2
1 nn aa
n
S +=

7. Example:
Find the sum:
1, 3, 5, 7
DON’T just add…use the formula
)(
2
1 nn aa
n
S +=

8. Summation Notation
∑=
+
3
1
)15(
n
n

9. Write the series in summation notation:
1. 3 + 6 + 9 +…for 33 terms
2. 1 + 2 + 3 + …for n=6
3. 3 + 8 + 13 + 18 +…for n=9

10. Find the sum of the series:
1.
2.
3.
4.
∑=
−
10
1
)3(
n
n
∑=
+
3
1
)15(
n
n
∑=
+
4
1
)1
2
1
(
n
n
∑=
5
2
2
n
n

11. Homework
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