Applications of Sequences & Series (DP IB Maths: AI HL)

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Applications of Arithmetic 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.

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

Examiner Tip

  • Exam questions won't always tell you to use sequences and series methods, practice spotting them by looking for clues in the question
  • If a given amount is repeated periodically then it is likely the question is on arithmetic sequences or series  

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

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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

Examiner Tip

  • Exam questions won't always tell you to use sequences and series methods, practice spotting them by looking for clues in the question
  • If a given amount is changing by a percentage or multiple then it is likely the question is on geometric sequences or series  

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

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Amber

Author: Amber

Expertise: Maths

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.