Top Rated by Parents/Students Nationwide
07478355331
Introduction to Sequences
Introduction to Sequences
What are sequences?
A sequence is an ordered set of (usually) numbers
Each number in a sequence is called a
term
The
location
of a
term
within a
sequence
is called its
position
The letter
n
is often used for (an unknown)
position
Subscript notation is used to talk about a particular term
a
1
would be the
first
term in a sequence
a
7
would be the
seventh
term
a
n
would be the
n
th
term
What is a position-to-term rule?
A
position-to-term
rule gives the
n
th
term of a sequence in terms of
n
This is a very powerful piece of mathematics
With a position-to-term rule the
100
th
term of a sequence can be found without having to know or work out the first 99 terms!
What is a term-to-term rule?
A
term-to-term
rule gives the
(n+1)
th
term in terms of the
n
th
term
ie
a
n+1
is given in terms of
a
n
If a term is known, the next one can be worked out
How do I use the position-to-term and term-to-term rules?
These can be used to generate a sequence
From a given sequence the rules can be deduced
Recognising and being aware of the types of sequences helps
Linear and quadratic sequences
Geometric sequences
Fibonacci sequences
Other sequences
Exam Tip
Write the position numbers above (or below) each term in a sequence
This will make it much easier to recognise and spot common types of sequence
Worked example
1. Number
Number Toolkit
Mathematical Operations
Negative Numbers
Money Calculations
Number Operations
Related Calculations
Counting Principles
Prime Factors, HCF & LCM
Types of Number
Prime Factor Decomposition
HCF & LCM
Powers, Roots & Standard Form
Powers, Roots & Indices
Standard Form
Fractions
Basic Fractions
Operations with Fractions
Percentages
Basic Percentages
Working with Percentages
Simple & Compound Interest, Growth & Decay
Interest & Depreciation
Exponential Growth & Decay
Fractions, Decimals & Percentages
Converting between FDP
Converting between FDP
Rounding, Estimation & Bounds
Rounding & Estimation
Bounds
Surds
Simplifying Surds
Rationalising Denominators
Using a Calculator
Using a Calculator
2. Algebra
Algebra Toolkit
Algebraic Notation & Vocabulary
Algebra Basics
Algebraic Roots & Indices
Algebraic Roots & Indices
Expanding Brackets
Expanding Single Brackets
Expanding Multiple Brackets
Factorising
Factorising
Factorising Quadratics
Quadratics Factorising Methods
Completing the Square
Completing the Square
Rearranging Formulae
Rearranging Formulae
Algebraic Proof
Algebraic Proof
Linear Equations
Solving Linear Equations
Solving Quadratic Equations
Solving Quadratic Equations
Quadratic Equation Methods
Simultaneous Equationsr
Simultaneous Equations
Iteration
Iteration
Forming & Solving Equations
Forming Equations
Equations & Problem Solving
Functions
Functions Toolkit
Composite & Inverse Functions
Coordinate Geometrys
Coordinates
Coordinate Geometry
Linear Graphs y = mx + c
Straight Line Graphs (y = mx + c)
Parallel & Perpendicular Lines
Graphs of Functions
Types of Graphs
Graphical Solutions
Trig Graphs
Equation of a Circle
Equation of a Circle
Equation of a Tangents
Estimating Gradients & Areas under Graphs
Finding Gradients of Tangents
Finding Areas under Graphs
Real-Life Graphs
Distance-Time & Speed-Time Graphs
Conversion Graphs
Rates of Change of Graphs
Solving Inequalities
Solving Linear Inequalities
Conversion Graphs
Solving Quadratic Inequalities
Graphing Inequalities
Graphing Inequalities
Transformations of Graphs
Reflections of Graphs
Sequences
Introduction to Sequences
Types of Sequences
Linear Sequences
Quadratic Sequences
3. Ratio, Proportion & Rates of Change
Ratio Toolkit
Simple Ratio
Working with Proportion
Ratio Problem Solving
Multiple Ratios
Direct & Inverse Proportions
Direct & Inverse Proportion
Standard & Compound Units
Time
Unit Conversions
Compound Measures
Exchange Rates & Best Buys
Exchange Rates & Best Buys
4. Geometry & Measures
Geometry Toolkit
Symmetry
2D & 3D Shapes
Plans & Elevations
Angles in Polygons & Parallel Lines
Basic Angle Properties
Angles in Polygons
Angles in Parallel Lines
Bearings, Scale Drawing, Constructions & Loci
Bearings
Scale & Maps
Constructing Triangles
Constructions & Loci
Circle Theorems
Angles at Centre & Semicircles
Chords & Tangents
Cyclic Quadrilaterals
Segment Theorems
Circle Theorem Proofs
Area & Perimeter
Area & Perimeter
Problem Solving with Areas
Circles, Arcs & Sectors
Area & Circumference of Circles
Arcs & Sectors
Volume & Surface Area
Volume
Surface Area
Congruence, Similarity & Geometrical Proof
Congruence
Similarity
Geometrical Proof
Area & Volume of Similar Shapes
Similar Area & Volumes
Right-Angled Triangles – Pythagoras & Trigonometry
Pythagoras Theorem
Right-Angled Trigonometry
Exact Trig Values
Sine, Cosine Rule & Area of Triangles
Sine & Cosine Rules
Area of a Triangle
Applications of Trigonomet
3D Pythagoras & Trigonometry
3D Pythagoras & Trigonometry
Vectors
Introduction to Vectors
Working with Vectors
Transformations
Translations
Reflections
Rotations
Enlargements
Combination of Transformations
5. Probability
Probability Toolkit
Basic Probability
Relative & Expected Frequency
Simple Probability Diagrams
Frequency Trees
Set Notation & Venn Diagrams
Tree Diagrams
Tree Diagrams
Combined & Conditional Probability
Combined Probability
Conditional Probability
Combined Conditional Probabilities
6. Statistics
Statistics Toolkit
Mean, Median & Mode
Averages from Tables
Range & Quartiles
Comparing Distributions
Population & Sampling
Statistical Diagrams
Bar Charts & Pictograms
Pie Charts
Time Series Graphs
Working with Statistical Diagrams
Histograms
Histograms
Cumulative Frequency & Box Plots
Cumulative Frequency Diagrams
Box Plots
Scatter Graphs & Correlation
Scatter Graphs
