Homework Questions
Arithmetic Series
Mrs. Ramsey
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)

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 +…
Finite Sequence

2, 11, 20, 29, 38, 47

Write the related series:

Evaluate the series:

An arithmetic series is a series whose
terms form an arithmetic sequence.

Sum of a Finite Arithmetic Series:
n
 S 
(a1  a n )
n
2
a1: 1st term
 an: nth term
 n: number of terms

Example:

Find the sum:
1, 3, 5, 7
 DON’T just add…use the formula

Sn 
n
(a1  a n )
2
Summation Notation
3
(
5
n

1
)

n 1
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
Find the sum of the series:
3
1.
 (5n  1)
n 1
10
2.
 (n  3)
n 1
4
1
(
3.  2 n  1)
n 1
5
4.
2
n

n2
Homework

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