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Sequences and Series involves number patterns: (2) Finding the sum of a section of the list of numbers (series) There are two general types of number patterns
at level 2: (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) 

1 
Overview
Overview of sequences and number patterns, Sequence notation using <> mapping notation and terms: t_{1}, t_{2}, t_{3}, t_{4... }continuing sequences using mapping notation. Recursive sequences: continuing recursive sequences & forming a recursive formula. 
Achievement criteria  I Can Do's General sequences Ex25.01, Class notes, Blank notes 
Fibonacci Sequence at http://nlvm.usu.edu Explore the Fibonacci sequence and the golden ratio. Theta pg 117 
2 
Sigma notation
Using sigma notation: Upper & lower limits, Terms, calculating a sum. Writing a sum in sigma notation. 
Class notes, Blank notes Sigma notation: Ex25.03 
Theta pg 118

3 
Arithmetic Sequences
Continuing an arithmetic sequence with a first term 'a' and common DIFFERENCE 'd'. Graphing arithmetic sequences. 
Ex26.01 
Theta pg 119 
4 
Arithmetic Sequences (cont)
Calculating 'a' & 'd' using simultaneous equations given two terms 
Ex26.02 
Links to Guru maths website sequences, Arithmetic, Geometric, ConvergenceTheta pg 120 
5 
Arithmetic series
Finding the sum of an arithmetic sequence. 
Ex26.03 
Links to Maths tutorial websites Sequences, Series, Arithmetic, Geometric,Theta pg 120 
6 
Arithmetic Applications
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? 
Ex26.04 
Theta pg 121 & 122 
7 
Geometric Sequences
Continuing a geometric sequence with a first term 'a' and common RATIO 'r'. Graphing arithmetic sequences. 
Ex27.01 
Theta pg 123 
8 
Geometric Sequences
(cont)
Calculating 'a' & 'r' using simultaneous equations given two terms. Using Logs to calculate 'n' given 'a' and 'r' 
Ex27.02 
Theta pg 124 
9 
Geometric Series
Finding the sum of an geometric sequence. 
Ex27.03 
Theta pg 125 
10 
Geometric Applications
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? 
Ex27.04 
Theta pg 126 
11 
Sum to infinity
When a geometric series has a common ratio between 1 and 1 (exclusive) a sum to infinity is a finite value S_{infinity} = ^{a} / _{1r } Sum to infinity 2 (JW) and Mrs Adairs Sum to infinity Sum to infinity powerpoint (web version)

Class notes, Blank notes Simple sum to infinity Ex27.05 Application problems Ex27.06 
Theta pg 126 
12 
Investment Applications
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) 
Ex28.01 Ex28.02 Ex28.03 
Theta pg 127 & 128 
13 
Revision Maths tutorial websites Sequences, Series, Arithmetic, Geometric, 
Revision test pg 411 
Theta pg 129 & 130 
14 
TEST 

