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CIE AS Maths: Pure 1

Revision Notes

Home / AS / Maths: Pure 1 / CIE / Revision Notes / 4. Sequences & Series / 4.3 Geometric Progressions / 4.3.1 Geometric Sequences


4.3.1 Geometric Sequences


What do I need to know about geometric progressions?

  • In a geometric progression (also called geometric sequence) there is a common ratio between consecutive terms in the sequence

Geom Seq Illustr, A Level & AS Level Pure Maths Revision Notes

  • You need to know the nth term formula for a geometric progression
begin mathsize 22px style u subscript n equals a r to the power of n minus 1 end exponent end style
    • a is the first term
    • r is the common ratio

Exam Tip

  • The formula is given in the formula booklet
  • If you know two terms in a geometric sequence you can find a and d using simultaneous equations. 

Geom Seq Simult, A Level & AS Level Pure Maths Revision Notes

Worked Example

Geom Seq Example, A Level & AS Level Pure Maths Revision Notes



  • 1. Algebra & Functions
    • 1.1 Quadratics
      • 1.1.1 Expanding Brackets
        • 1.1.2 Quadratic Graphs
          • 1.1.3 Discriminants
            • 1.1.4 Completing the square
              • 1.1.5 Solving Quadratic Equations
                • 1.1.6 Further Solving Quadratic Equations (Hidden Quadratics)
                • 1.2 Inequalities & Simultaneous Equations
                  • 1.2.2 Linear Simultaneous Equations - Substitution
                    • 1.2.3 Quadratic Simultaneous Equations
                      • 1.2.4 Linear Inequalities
                        • 1.2.5 Quadratic Inequalities
                          • 1.2.6 Inequalities on Graphs
                          • 1.3 Functions
                            • 1.3.1 Language of Functions
                              • 1.3.2 Composite Functions
                                • 1.3.3 Inverse Functions
                                • 1.4 Graphs of Functions
                                  • 1.4.1 Sketching Polynomials
                                    • 1.4.2 Reciprocal Graphs - Sketching
                                      • 1.4.3 Solving Equations Graphically
                                        • 1.4.4 Proportional Relationships
                                        • 1.5 Transformations of Functions
                                          • 1.5.1 Translations
                                            • 1.5.2 Stretches
                                              • 1.5.3 Reflections
                                              • 1.6 Combinations of Transformations
                                                • 1.6.1 Combinations of Transformations
                                                • 1.7 Modelling with Functions
                                                  • 1.7.1 Modelling with Functions
                                                • 2. Coordinate Geometry
                                                  • 2.1 Equation of a Straight Line
                                                    • 2.1.1 Basic Coordinate Geometry
                                                      • 2.1.2 Parallel & Perpendicular Gradients
                                                        • 2.1.3 Equation of a Straight Line
                                                          • 2.1.4 Modelling with Straight Lines
                                                          • 2.2 Circles
                                                            • 2.2.1 Equation of a Circle
                                                              • 2.2.2 Finding the Centre & Radius
                                                                • 2.2.3 Bisection of Chords
                                                                  • 2.2.4 Angle in a Semicircle
                                                                    • 2.2.5 Radius & Tangent
                                                                  • 3. Trigonometry
                                                                    • 3.1 Basic Trigonometry
                                                                      • 3.1.1 Trigonometry - Definitions
                                                                        • 3.1.2 Right-Angled Triangles
                                                                          • 3.1.3 Non-Right-Angled Triangles
                                                                          • 3.2 Trigonometric Functions
                                                                            • 3.2.1 Graphs of Trigonometric Functions
                                                                              • 3.2.2 Transformations of Trigonometric Functions
                                                                              • 3.3 Circular Measure (Radians)
                                                                                • 3.3.1 Radian Measure
                                                                                  • 3.3.2 Trigonometry Exact Values
                                                                                  • 3.4 Trigonometric Equations
                                                                                    • 3.4.1 Trigonometry - Simple Identities
                                                                                      • 3.4.2 Linear Trigonometric Equations
                                                                                        • 3.4.3 Quadratic Trigonometric Equations
                                                                                          • 3.4.4 Strategy for Trigonometric Equations
                                                                                          • 3.5 Modelling with Trigonometric Functions
                                                                                            • 3.5.1 Modelling with Trigonometric Functions
                                                                                          • 4. Sequences & Series
                                                                                            • 4.1 Binomial Expansion
                                                                                              • 4.1.1 Binomial Expansion
                                                                                              • 4.2 Arithmetic Progressions
                                                                                                • 4.2.1 Arithmetic Sequences
                                                                                                  • 4.2.2 Arithmetic Series
                                                                                                  • 4.3 Geometric Progressions
                                                                                                    • 4.3.1 Geometric Sequences
                                                                                                      • 4.3.2 Geometric Series
                                                                                                      • 4.4 Further Sequences & Series
                                                                                                        • 4.4.1 Language of Sequences & Series
                                                                                                          • 4.4.2 Sigma Notation
                                                                                                            • 4.4.3 Recurrence Relations
                                                                                                              • 4.4.4 Modelling with Sequences & Series
                                                                                                            • 5. Differentiation
                                                                                                              • 5.1 Differentiation
                                                                                                                • 5.1.1 Definition of Gradient
                                                                                                                  • 5.1.2 Definition of Derivatives
                                                                                                                    • 5.1.3 Differentiating Powers of x
                                                                                                                      • 5.1.4 Chain Rule
                                                                                                                      • 5.2 Applications of Differentiation
                                                                                                                        • 5.2.1 Gradients, Tangents & Normals
                                                                                                                          • 5.2.2 Increasing & Decreasing Functions
                                                                                                                            • 5.2.3 Second Order Derivatives
                                                                                                                              • 5.2.4 Stationary Points & Turning Points
                                                                                                                                • 5.2.5 Sketching Gradient Functions
                                                                                                                                  • 5.2.6 Modelling with Differentiation inc. Optimisation
                                                                                                                                    • 5.2.7 Connected Rates of Change
                                                                                                                                  • 6. Integration
                                                                                                                                    • 6.1 Integration
                                                                                                                                      • 6.1.1 Fundamental Theorem of Calculus
                                                                                                                                        • 6.1.2 Integrating Powers of x
                                                                                                                                          • 6.1.3 Definite Integration
                                                                                                                                            • 6.1.4 Reverse Chain Rule
                                                                                                                                              • 6.1.5 Improper Integrals
                                                                                                                                              • 6.2 Further Integration
                                                                                                                                                • 6.2.1 Area Under a Curve
                                                                                                                                                  • 6.2.2 Area between a curve and a line
                                                                                                                                                    • 6.2.3 Area between 2 curves
                                                                                                                                                      • 6.2.4 Volumes of Revolution
                                                                                                                                                        • 6.2.5 Adding and Subtracting Volumes
                                                                                                                                                          • 6.2.6 Modelling with Volumes of Revolution


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                                                                                                                                                        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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