DAY 4 Introduction to sequences. PI 11ArithmeticAndGeom.notebook

DAY 4 Introduction to sequences. PI 11ArithmeticAndGeom.notebook
DAY 4
February 20, 2017
February 17/18, 2017
Did you Copy notes on FACTORIALS?
CLASS OPENER (Do NOW): UNIT 8: Sequences and Series
PI11: Arithmetic and Geometric Sequences.
Apr 10­4:46 PM
Feb 11­8:33 AM
U8: PI 11 Arithmetic and Geometric Sequences
REVIEW: Writing numbers using expressions
Use variables to write :
FIND THE MISSING TERMS IN THE SEQUENCE GIVEN BELOW
Any integer An Even integer An Odd integer Three consecutive integers Three consecutive odd integers _____; _____; an ; _______; _______
Three consecutive even integers Any two odd integers back in time ...... in algebra Given two points (2, 4) ; (­3 , 5) find the slope :
an=an­1 + 18
in present time ....... given a sequence of 5 terms 2, 4, 6, 8, 10
how would you identify each term using variables ?
an+1=an+18
Apr 10­4:54 PM
Apr 10­4:55 PM
Definition of a SEQUENCE:
Definition of a SEQUENCE:
A sequence is an ordered list of numbers. Each member of a sequence is called a term. Terms of a sequence are arranged in a pattern. A formula that defines the terms of the sequence is called an explicit formula. A sequence is an ordered list of numbers. Each member of a sequence is called a term. Terms of a sequence are arranged in a pattern. A formula that defines the terms of the sequence is called an explicit formula. EX 2. Write the first four terms of a sequence given by the explicit formula: EX 2. Write the first four terms of a sequence given by the explicit formula: n an
PER C
n an
Apr 10­4:55 PM
Apr 10­4:55 PM
1
DAY 4 Introduction to sequences. PI 11ArithmeticAndGeom.notebook
February 20, 2017
PER. A
Apr 14­8:59 AM
Apr 14­8:59 AM
A sequence can also be defined by a recursive formula. Find the first four terms in each sequence given the formula.
a)
b)
­1
With a recursive formula, one or more previous terms are used to generate the next term and one or more first terms must be known. [You may have seen a type of recursive formula called "NOW/NEXT" statements in the past]
EX 4. Write the first five terms of a sequence given by a recursive formula a2=
a3 =
a4=
a5 = Apr 2­1:50 PM
EX.5.: The Fibonacci sequence is defined recursively as follows: Write the first 6 terms of this sequence.
Apr 10­4:58 PM
Apr 10­4:58 PM
Explicit and Recursive Formula
Find the next three terms in each sequence and write the recursive and explicit formula for the given sequence. -5 , -1, 3, 7, ...
0, 3, 8, 15, 24, ...
Apr 10­4:58 PM
2
DAY 4 Introduction to sequences. PI 11ArithmeticAndGeom.notebook
Explicit and Recursive Formula
Find the next three terms in each sequence and write the recursive and explicit formula for the given sequence. February 20, 2017
Explicit and Recursive Formula
Find the next three terms in each sequence and write the recursive and explicit formula for the given sequence. 0, 3, 8, 15, 24, ...
-5 , -1, 3, 7, ...
0, 3, 8, 15, 24, ...
Apr 2­11:17 AM
Apr 10­4:58 PM
Find the next three terms in a sequence given and find the nth term formula for each sequence :
Find the next three terms in a sequence given and find the nth term formula for each sequence :
1 , 1 , 3 , 1, 5 , ...
2 2 8 4 32
1 , 1 , 3 , 1, 5 , ...
2 2 8 4 32
Feb 27­9:10 AM
Feb 27­9:10 AM
Which sequence is finite and which one is infinite
1 , 4, 7, 10, ..., an=3n-2, ...
1 , 4, 7, 10, ...,28
Feb 26­9:43 PM
Mar 17­2:19 PM
3
DAY 4 Introduction to sequences. PI 11ArithmeticAndGeom.notebook
Mar 17­2:19 PM
Arithmetic Sequence
February 20, 2017
Mar 17­2:20 PM
PI 11:
Lesson 8.1. - 8.2. Finding terms of a sequence and
Arithmetic Sequences
>>>PRACTICE sheet Additional practice:
>>>Section 8.1: Page 563/ 15, 17, 21, 23, 45, 47, 49, 51, 55, 59, 63, 65, 71, 73
>>>Section 8.2: Page 573/ 5, 13, 15, 21, 25, 31, 37, 41
Mar 17­2:21 PM
Mar 17­2:16 PM
4