Main Ideas/Questions Notes/Examples A set of numbers with...
4
Main Ideas/Questions Notes/Examples Sequence Finite Sequence Example: Infinite Sequence Example: Term Notation • The first term in a sequence is denoted _______. • Each subsequent term is denoted _______, where _____ is the term number in the sequence. Example: Given {1, 5, 9, 13, 17, …}, identify the following term values: 1 : a _______ 4 : a _______ 9 : a _______ 12 : a _______ Sequences as Functions Since each term value is paired with exactly one term number, a sequence is a function with the following properties: The domain is the set of ___________ _________________. The range is the set of ___________ _________________. In an infinite set, the domain is the the set of ______________________________ Recursive Formulas The Fibonnaci Sequence: ___________________________________________ 1 2 In this sequence, a = 0 , a = 1 , then for each subsequent term, _____________________________________ Examples Directions: Find the first 5 terms of each sequence. 1. 1 1 14; 9 n n a a a − = = + (for 2 n ≥ ) 2. 1 1 6; 2 5 n n a a a − = = − (for 2 n ≥ ) Name: ____________________________________________________ Class: ________________________________ Date: ________________________________ Topic: ____________________________________________________ n 1 2 3 4 5 n a 1 5 9 13 17 © Gina Wilson (All Things Algebra), 2016 AFM Name: Unit 5 Day 1 Notes: Sequences & Series Date: A set of numbers with a particular order or pattern. Each number is called a "term". A sequence with a limited number of terms. A sequence with unlimited terms. A rule in which one or more previous terms are used to generate the next term.
Transcript of Main Ideas/Questions Notes/Examples A set of numbers with...
Main Ideas/Questions Notes/Examples
Sequence
Finite Sequence Example:
Infinite Sequence Example:
Term Notation
• The first term in a sequence is denoted _______.
• Each subsequent term is denoted _______, where _____ is theterm number in the sequence.
Example: Given {1, 5, 9, 13, 17, …}, identify the following term values:
1 :a _______ 4 :a _______ 9 :a _______ 12 :a _______
Sequences as Functions
Since each term value is paired with exactly one term number, a sequence is a function with the following properties:
The domain is the set of ___________ _________________.
The range is the set of ___________ _________________.
In an infinite set, the domain is the the set of ______________________________
Recursive Formulas
The Fibonnaci Sequence: ___________________________________________
1 2In this sequence, a = 0 , a = 1 , then for each subsequent term,
_____________________________________
Examples Directions: Find the first 5 terms of each sequence. 1. 1 114; 9n na a a −= = + (for 2n ≥ ) 2. 1 16; 2 5n na a a −= = − (for 2n ≥ )
Name: ____________________________________________________
Class: ________________________________
Date: ________________________________
Topic: ____________________________________________________
n 1 2 3 4 5 na 1 5 9 13 17
© Gina Wilson (All Things Algebra), 2016
AFM Name: Unit 5 Day 1 Notes: Sequences & Series Date:
A set of numbers with a particular order or pattern. Each number is called a "term".A sequence with a limited number of terms.
A sequence with unlimited terms.
A rule in which one or more previous terms are used to generate the next term.
72
23. 11
6354;3
nn
aa a − += = (for 2n ≥ )
4. n n n− −
(for 3n ≥ )
Directions: Write a rule for each sequence. Then give the next 3 terms. 5. { }4, 11, 32, 95, 284, ... 6. { }100, 60, 40, 30, 25, ...
Explicit Formulas
Examples Directions: Find the first 5 terms of each sequence. 7. 7( 3)na n= −
8.11
3
n
na+
=
9. 24na n= − 10. 2 ( 5)na n n= +
11. 1( 2)nna−= − 12. 2( 4)na n= −
Directions: Write a rule for each sequence. Then give the next 3 terms.13. { }7, 9, 11, 13, 15, ...− − − − − 14. { }3, 6, 11, 18, 27, ...
15. 52, , 3, , 4, ...
16. { }1, 2, 3, 2, 5, ...
© Gina Wilson (All Things Algebra), 2016
1 1 23, 4 ;= = = ⋅a a a a a
2
A rule in which the nth term is defined as a function of n. (Previous terms not needed)
Main Ideas/Questions Notes/Examples
SERIESSERIESSERIESSERIES Sequence { }1, 2, 3, 4 { }3, 6, 9, 12 ,... 1 1 1 1, , , ,...
2 4 8 16
Series
PARTIAL SUMSPARTIAL SUMSPARTIAL SUMSPARTIAL SUMS Directions: Find the partial sum for each given sequence. 1. { };1, 2, 3, 4, 5,... find 9S 2. { };4, 7, 13, 25, 49,... find 4S
3. { };1, 4, 9, 16, 25,... find 6S 4. 1 1 1 1 ;1, , , , ,...2 3 4 5
find 3S
SUMMATIONSUMMATIONSUMMATIONSUMMATION NotationNotationNotationNotation
A way to represent a series using the greek letter Σ to denote the sum.
Find the sum of the series above:
EXAMPLESEXAMPLESEXAMPLESEXAMPLES
Directions: Expand each series and evaluate.
5. ( )12
11
nn
=−∑
6. ( )7
13
nn
=−∑
Name: ____________________________________________________
Class: ________________________________
Date: ________________________________
Topic: ____________________________________________________
© Gina Wilson (All Things Algebra), 2016
The sum of the terms in a sequence.
The sum of a specified number of terms.
7. ( )4
15 2
kk
=+∑
8. ( )9
22 7
aa
=−∑
9. ( )5
2
1yy y
=+∑
10. 38
2 2c
c=
∑
11. ( )6
2
21
mm
=−∑
12. ( )8 2
43 4
pp
=
⋅ −∑
13. ( )4
2
2
152 x
x=
⋅ −∑
© Gina Wilson (All Things Algebra), 2016
