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IB DP Maths: AI SL

Revision Notes

Home / DP / Maths: AI SL / IB / Revision Notes / 1. Number & Algebra / 1.2 Sequences & Series / 1.2.4 Applications of Sequences & Series


1.2.4 Applications of Sequences & Series


Many real-life situations can be modelled using sequences and series, including but not limited to: patterns made when tiling floors; seating people around a table; the rate of change of a population; the spread of a virus and many more.

Applications of Arithmetic Sequences & Series

What do I need to know about applications of arithmetic 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 to model the situation
    • If a sequence seems to fit the pattern of an arithmetic sequence it can be said to be modelled by an arithmetic sequence
    • The scenario can be modelled using the given information and the formulae from the formula booklet
  • A common application of arithmetic sequences and series is simple interest
    • Simple interest is when an initial investment is made and then a percentage of the initial investment is added to this amount on a regular basis (usually per year)
  • Arithmetic sequences can be used to make estimations about how something will change in the future

Worked Example

Jasper is saving for a new car. He puts USD $100 into his savings account and then each month he puts in USD $10 more than the month before. Jasper needs USD $1200 for the car. Assuming no interest is added, find, 

 

i)
the amount Jasper has saved after four months,

ai-sl-1-2-4-apps-of-as-a

 

ii)
the month in which Jasper reaches his goal of USD $1200.

ai-sl-1-2-4-apps-of-as-b

Applications of Geometric Sequences & Series

What do I need to know about applications of geometric sequences and series?

  • 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 to model the situation
    • If a sequence seems to fit the pattern of a geometric sequence it can be said to be modelled by a geometric sequence
    • The scenario can be modelled using the given information and the formulae from the formula booklet
  • A common application of geometric sequences and series is compound interest
    • Compound interest is when an initial investment is made and then interest is paid on the initial amount and on the interest already earned on a regular basis (usually every year)
  • Geometric sequences can be used to make estimations about how something will change in the future
  • The questions won’t always tell you to use sequences and series methods, so be prepared to spot ‘hidden’ sequences and series questions
    • Look out for questions on savings accounts, salaries, sales commissions, profits, population growth and decay, spread of bacteria etc

Worked Example

A new virus is circulating on a remote island. On day one there were 10 people infected, with the number of new infections increasing at a rate of 40% per day.

 

a)
Find the expected number of people newly infected on the 7th day.

ai-sl-1-2-4-apps-of-gs-i

 

b)
Find the expected number of infected people after one week (7 days), assuming no one has recovered yet.

ai-sl-1-2-4-apps-of-gsii



  • 1. Number & Algebra
    • 1.1 Number Toolkit
      • 1.1.1 Standard Form
        • 1.1.2 Exponents & Logarithms
          • 1.1.3 Approximation & Estimation
            • 1.1.4 GDC: Solving Equations
            • 1.2 Sequences & Series
              • 1.2.1 Language of Sequences & Series
                • 1.2.2 Arithmetic Sequences & Series
                  • 1.2.3 Geometric Sequences & Series
                    • 1.2.4 Applications of Sequences & Series
                    • 1.3 Financial Applications
                      • 1.3.1 Compound Interest & Depreciation
                        • 1.3.2 Amortisation & Annuities
                      • 2. Functions
                        • 2.1 Linear Functions & Graphs
                          • 2.1.1 Equations of a Straight Line
                          • 2.2 Further Functions & Graphs
                            • 2.2.1 Functions
                              • 2.2.2 Graphing Functions
                                • 2.2.3 Properties of Graphs
                                • 2.3 Modelling with Functions
                                  • 2.3.1 Linear & Piecewise Models
                                    • 2.3.2 Quadratic & Cubic Models
                                      • 2.3.3 Exponential Models
                                        • 2.3.4 Direct & Inverse Variation
                                          • 2.3.5 Sinusoidal Models
                                            • 2.3.6 Strategy for Modelling Functions
                                          • 3. Geometry & Trigonometry
                                            • 3.1 Geometry Toolkit
                                              • 3.1.1 Coordinate Geometry
                                                • 3.1.2 Arcs & Sectors
                                                • 3.2 Geometry of 3D Shapes
                                                  • 3.2.1 3D Coordinate Geometry
                                                    • 3.2.2 Volume & Surface Area
                                                    • 3.3 Trigonometry
                                                      • 3.3.1 Pythagoras & Right-Angled Triganometry
                                                        • 3.3.2 Non Right-Angled Trigonometry
                                                          • 3.3.3 Applications of Trigonometry & Pythagoras
                                                          • 3.4 Voronoi Diagrams
                                                            • 3.4.1 Voronoi Diagrams
                                                              • 3.4.2 Toxic Waste Dump Problem
                                                            • 4. Statistics & Probability
                                                              • 4.1 Statistics Toolkit
                                                                • 4.1.1 Sampling & Data Collection
                                                                  • 4.1.2 Statistical Measures
                                                                    • 4.1.3 Frequency Tables
                                                                      • 4.1.4 Linear Transformations of Data
                                                                        • 4.1.5 Outliers
                                                                          • 4.1.6 Univariate Data
                                                                            • 4.1.7 Interpreting Data
                                                                            • 4.2 Correlation & Regression
                                                                              • 4.2.1 Bivariate data
                                                                                • 4.2.2 Correlation Coefficients
                                                                                  • 4.2.3 Linear Regression
                                                                                  • 4.3 Probability
                                                                                    • 4.3.1 Probability & Types of Events
                                                                                      • 4.3.2 Conditional Probability
                                                                                        • 4.3.3 Sample Space Diagrams
                                                                                        • 4.4 Probability Distributions
                                                                                          • 4.4.1 Discrete Probability Distributions
                                                                                            • 4.4.2 Expected Values
                                                                                            • 4.5 Binomial Distribution
                                                                                              • 4.5.1 The Binomial Distribution
                                                                                                • 4.5.2 Calculating Binomial Probabilities
                                                                                                • 4.6 Normal Distribution
                                                                                                  • 4.6.1 The Normal Distribution
                                                                                                    • 4.6.2 Calculations with Normal Distribution
                                                                                                    • 4.7 Hypothesis Testing
                                                                                                      • 4.7.1 Hypothesis Testing
                                                                                                        • 4.7.2 Chi-squared Test for Independence
                                                                                                          • 4.7.3 Goodness of Fit Test
                                                                                                            • 4.7.4 The t-test
                                                                                                          • 5. Calculus
                                                                                                            • 5.1 Differentiation
                                                                                                              • 5.1.1 Introduction to Differentiation
                                                                                                                • 5.1.2 Applications of Differentiation
                                                                                                                  • 5.1.3 Modelling with Differentiation
                                                                                                                  • 5.2 Integration
                                                                                                                    • 5.2.1 Trapezoid Rule: Numerical Integration
                                                                                                                      • 5.2.2 Introduction to Integration
                                                                                                                        • 5.2.3 Applications of Integration


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                                                                                                                      Author: Amber

                                                                                                                      Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.


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