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Edexcel International AS Maths: Pure 2

Revision Notes

Home / International AS / Maths: Pure 2 / Edexcel / Revision Notes / 4. Sequences & Series / 4.5 Modelling with Sequences & Series / 4.5.1 Modelling with Sequences & Series


4.5.1 Modelling with Sequences & Series


Modelling with Sequences & Series

What do I need to know about modelling with sequences and series?

  • Many real-life situations can be modelled using sequences and series
  • If a quantity is changing repeatedly by having a fixed amount added to or subtracted from it then the use of arithmetic sequences and arithmetic series is appropriate

Model Seq Ser Illustr 1, A Level & AS Level Pure Maths Revision Notes

  • If a quantity is changing repeatedly by a fixed percentage, or by being multiplied repeatedly by a fixed amount, then the use of geometric sequences and geometric series is appropriate

 Model Seq Ser Illustr 2, A Level & AS Level Pure Maths Revision Notes

 

Exam Tip

  • Remember, an exam question won't always tell you to use sequence and series methods, so you've got to be able to spot 'hidden' sequence and series questions.
  • To help you do this, be suspicious of questions about savings accounts, salaries, sales commissions, profits and the like – these are often sequence and series questions in disguise!

Worked Example

Model Seq Ser Example, A Level & AS Level Pure Maths Revision Notes



  • 1. Proof
    • 1.1 Proof
      • 1.1.1 Language of Proof
        • 1.1.2 Proof by Deduction
          • 1.1.3 Proof by Exhaustion
            • 1.1.4 Disproof by Counter Example
          • 2. Algebra & Functions
            • 2.1 Polynomials
              • 2.1.1 Polynomial Division
                • 2.1.2 Factor & Remainder Theorem
                  • 2.1.3 Factorisation
                • 3. Coordinate Geometry
                  • 3.1 Circles
                    • 3.1.1 Equation of a Circle
                      • 3.1.2 Finding the Centre & Radius
                        • 3.1.3 Bisection of Chords
                          • 3.1.4 Angle in a Semicircle
                            • 3.1.5 Radius & Tangent
                          • 4. Sequences & Series
                            • 4.1 Binomial Expansion
                              • 4.1.1 Binomial Expansion
                              • 4.2 Arithmetic Sequences & Series
                                • 4.2.1 Arithmetic Sequences
                                  • 4.2.2 Arithmetic Series
                                  • 4.3 Geometric Sequences & Series
                                    • 4.3.1 Geometric Sequences
                                      • 4.3.2 Geometric Series
                                      • 4.4 Sequences & Series
                                        • 4.4.1 Language of Sequences & Series
                                          • 4.4.2 Sigma Notation
                                            • 4.4.3 Recurrence Relations
                                            • 4.5 Modelling with Sequences & Series
                                              • 4.5.1 Modelling with Sequences & Series
                                            • 5. Logs & Exponentials
                                              • 5.1 Laws of Logarithms
                                                • 5.1.1 Exponential Functions
                                                  • 5.1.2 Logarithmic Functions
                                                    • 5.1.3 Laws & Change of Base
                                                      • 5.1.4 Exponential Equations
                                                    • 6. Trigonometry
                                                      • 6.1 Trigonometric Equations
                                                        • 6.1.1 Trigonometry - Simple Identities
                                                          • 6.1.2 Linear Trigonometric Equations
                                                            • 6.1.3 Quadratic Trigonometric Equations
                                                              • 6.1.4 Strategy for Trigonometric Equations
                                                            • 7. Differentiation
                                                              • 7.1 Applications of Differentiation
                                                                • 7.1.1 Increasing & Decreasing Functions
                                                                  • 7.1.2 Stationary Points & Turning Points
                                                                    • 7.1.3 Sketching Gradient Functions
                                                                      • 7.1.4 Modelling with Differentiation inc. Optimisation
                                                                    • 8. Integration
                                                                      • 8.1 Integration
                                                                        • 8.1.1 Definite Integration
                                                                          • 8.1.2 Area Under a Curve
                                                                            • 8.1.3 Area between a curve and a line
                                                                              • 8.1.4 Area between 2 curves
                                                                                • 8.1.5 Trapezium Rule (Numerical Integration)


                                                                                DOWNLOAD PDF

                                                                              Author: Roger

                                                                              Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.


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