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Applications of Sequences & Series (DP IB Maths: AI HL)
Revision Note
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,
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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.
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