US 5248 Sequences & Series

Sequences and Series involves number patterns:
(1) Finding a particular number in the pattern (eg the 20th term)

(2) Finding the sum of a section of the list of numbers (series)

There are two general types of number patterns at level 2:
(1) Arithmetic sequences (a common difference - adding or subtracting a constant)

(2) Geometric sequences (a common multiplier - which can be a fraction)

The sum of all numbers in a geometric sequence can be found if the common multiplier is between 0 and 1(sum to infinity)

Word doc 07/03 Theta Homework Book (David Barton) Theta Text Book (David Barton)
Web link Geogebra java animation Powerpoint Excel Spreadsheet (allow macros)

1

Overview of sequences and number patterns, Sequence notation using <> mapping notation and terms: t₁, t₂, t₃, t_4... continuing sequences using mapping notation.

Recursive sequences: continuing recursive sequences & forming a recursive formula.

Achievement Criteria

Introduction to sequences

Achievement criteria | I Can Do's

General sequences Ex25.01,
Recursive Sequences Ex25.02,

Class notes, Blank notes

Achievement criteria

Fibonacci Sequence at http://nlvm.usu.edu Explore the Fibonacci sequence and the golden ratio.

kovalevsy.pdf

Theta pg 117

2

Using sigma notation: Upper & lower limits, Terms, calculating a sum. Writing a sum in sigma notation.

Class notes, Blank notes

Sigma notation: Ex25.03

Simplifying A

Theta pg 118

3

Continuing an arithmetic sequence with a first term 'a' and common DIFFERENCE 'd'.
Using the formula t_n = a + (n - 1)d
Finding a specific term t_n, finding a general term for an arithmetic sequence, calculating any one of 'a' 'd' 'n' and t_n given three other values

Graphing arithmetic sequences.

Class notes, Blank notes

Ex26.01

Algebra Fractions

Theta pg 119

4

Calculating 'a' & 'd' using simultaneous equations given two terms

Class notes, Blank notes

Ex26.02

Links to Guru maths website sequences, Arithmetic, Geometric, Convergence

Theta pg 120

5

Finding the sum of an arithmetic sequence.
Using the formula S_n = ⁿ/₂[2a + (n - 1)d]
Finding a specific sum S_n, calculating any one of 'a' 'd' 'n' and S_n given three other values

Class notes, Blank notes

Ex26.03

Links to Maths tutorial websites Sequences, Series, Arithmetic, Geometric,

Theta pg 120

6

Using arithmetic sequences and series to solve application. Read the problem carefully, extract the important information: a=? d=? Sum or term? What is the question asking for?

Class notes, Blank notes

Ex26.04

Theta pg 121 & 122

7

Continuing a geometric sequence with a first term 'a' and common RATIO 'r'.
Using the formula t_n = a*r^^{(n - 1)}
Finding a specific term t_n, finding a general term for an arithmetic sequence, calculating any one of 'a' 'd' 'n' and t_n given three other values

Graphing arithmetic sequences.

Geometric sequences (featuring Bad Jelly)  (web version) 

Class notes, Blank notes

Ex27.01

Theta pg 123

8

Calculating 'a' & 'r' using simultaneous equations given two terms.

Using Logs to calculate 'n' given 'a' and 'r'

Class notes, Blank notes

Ex27.02

Theta pg 124

9

Finding the sum of an geometric sequence.
Using the formula S_n = a(rⁿ - 1)/_(r-1)
Finding a specific sum S_n, calculating any one of 'a' 'r' 'n' and S_n given three other values

Geometric Series  (web version) 

Class notes, Blank notes

Ex27.03

Theta pg 125

10

Using geometric sequences and series to solve application. Read the problem carefully, extrach the important information: a=? d=? Sum or term? What is the question asking for?

Class notes, Blank notes

Ex27.04

Theta pg 126

11

When a geometric series has a common ratio between -1 and 1 (exclusive) a sum to infinity is a finite value

S_infinity = ^a / _1-r

Sum to infinity 2 (JW) and Mrs Adairs Sum to infinity

Sum to infinity powerpoint  (web version) 

Sum to infinity animation (maths on line)
Koch's snowflake - sum to infinity concept  | Image A | Image B | Image C

Class notes, Blank notes

Simple sum to infinity Ex27.05

Application problems Ex27.06

Theta pg 126

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An investment of a Principle 'P' for 'n' years at '15%' increase interest rate = P*(1.15)ⁿ (or for inflation)

An investment of a Principle 'P' for 'n' years at '15%' decrease interest rate = P*(0.85)ⁿ (or for depreciation)

Class notes, Blank notes

Ex28.01 Ex28.02 Ex28.03

Theta pg 127 & 128

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Revision

Maths tutorial websites Sequences, Series, Arithmetic, Geometric,

Revision test pg 411

Theta pg 129 & 130

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TEST