1. Objectives 1. 2.
Understand the difference between a finite and infinite series.
Write and evaluate an arithmetic series.

2. Understand the difference between Finite and Infinite Series
The sum of the terms of a sequence.
Finite Sequences & Series:
Can be counted and totaled (has an end).
Infinite Sequences & Series:
Cannot be counted and totaled (does not have an end).
Finite Sequence
6, 9, 12, 15, 18
Finite Series
Infinite Sequence
3, 7, 11, 15, . . .
Infinite Series

3. Example 1: Writing & Evaluating a Series
Use the finite sequence 2, 11, 20, 29, 38, 47.
Write the related series, and then evaluate.
Related Series: =
147
Example 1: Practice
21, 18, 15, 12, 9, 6, 3
, 99, 98, . . ., 95
, 19.6, 21.9, 24.2, 26.5
; 84
; 585
; 109.5

4. Arithmetic Series Sum of a Finite Arithmetic Series
A series whose terms form an arithmetic sequence.
When a sequence has many terms, or when you know only the 1st and last terms of the sequence, you can use a formula to evaluate the related series quickly.
Sum of a Finite Arithmetic Series
The sum Sn of a finite arithmetic series a1 + a2 + a an is
where a1 is the 1st term, an is the nth term, & n is the # of terms.

5. Example 2: Evaluating an Arithmetic Series
Use the formula to evaluate the series related to the following sequence: 5, 7, 9, 11, 13 52
(5 + 13) = =
2.5(18) = 45

6. Example 2: Practice
Each sequence has 8 terms. Evaluate each related series. 4. 32
5. 5, 13, 21, , 61
6. 1,765, 1,414, 1,063, , -692
264
4,292

7. Objectives 1. Discover the sum of the terms of an arithmetic series.2.
Discover the sum of the terms of an arithmetic series.
Interpret summation notation and be able to rewrite as a series.

8. explicit formula for the sequence
Using Summation Notation
You can use the summation symbol  to write a series.
Then you can use limits to indicate how many terms you are adding.
Limits are the least and greatest integral value of n.
upper limit,
greatest value of n.  3
n = 1
(5n + 1)
explicit formula for the sequence
lower limit,
least value of n.

9. Use summation notation to write the series
Example 3: Writing a Series in Summation Notation
Use summation notation to write the series
for 33 items.
1 • 3 = 3
2 • 3 = 6
3 • 3 = 9
The explicit formula for the sequence is ____. 3n 33 
The lower limit is ___.
The upper limit is ___. 1 = 3n 33 1

10. Example 3: Practice
Use summation notation to write each arithmetic series for the specified number of terms.  2n 4
n = 1
; n = 4
; n = 7
; n = 15 
(n + 4) 7
n = 1  7n 15
n = 1

11.   Example 4: Finding the Sum of a Series (5n + 1).3
(5n + 1).
n = 1
To expand a series from summation notation, substitute each value of n into the explicit formula and add the results.
Use the series a.
Find the number of terms in the series.
Since the values of n are 1, 2, & 3, there are ___ terms. 3 b.
Find the first and last terms of the series.
Term #1 =
(5n + 1) =
5(1) + 1 = 6
Term #3 =
(5n + 1) =
5(3) + 1 = 16 c.
Evaluate the series.  3
(5n + 1)
n = 1 =
5(1) + 1 +
5(2) + 1 +
5(3) + 1
6 +
11 + 16 33

12. Example 4: Practice
For each sum, find the number of terms, the first term, and the last term. Then evaluate the series.  5
(2n - 1)
n = 1
19.
21.
23.
5, 1, 9; 25  8
(7 - n)
n = 3
6, 4, -1; 9  10
n = 2
4n3

13. ? Example 5: Real-World Application Questions 1 + 4 + 16 + 64 + 256.
If Mary goes to the prom with Brian, he will be able to practice what he learned about sequences and series in Alg. 2 class.
The price of the tickets
Questions
4 hours of fun 1.
Is this series arithmetic, geometric, or neither?
geometric
1 date
16 cups of fruit punch
How many times Bobby tried to ask her but chickened out. 2.
Kayla, will you go to the prom with Bobby? ?