Applications of Sequences & Series (DP IB Analysis & Approaches (AA)): Revision Note
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Applications of Arithmetic Sequences & Series
How do I spot arithmetic sequences and series?
If a quantity is changing by repeatedly having a fixed amount added to or subtracted from it, then use arithmetic sequences and series
For example
simple interest (the same amount of interest is added to an initial amount each year)
stacking cups
planting trees
counting dots in a pattern
Examiner Tips and Tricks
If you don't spot an arithmetic sequence in the exam, you can still work out some parts by hand, but you won't have the 
and 
formulae to speed you up.
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
(a) the amount Jasper has saved after four months,
(b) the month in which Jasper reaches his goal of USD $1200.
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Applications of Geometric Sequences & Series
How do I spot geometric sequences and series?
If a quantity is changing by repeatedly being multiplied (or divided) by the same amount each time, use geometric sequences and series
For example
compound interest (interest each year is on the initial amount of money plus all the interest you've saved up to that point)
population growth
bacterial growth
radioactive decay
Examiner Tips and Tricks
If you don't spot a geometric sequence in the exam, you can still work out some parts by hand, but you won't have the and formulae to speed you up.
Worked Example
A new virus is circulating on a remote island.
On day one, there were 10 people infected. The number of new infections increases at a rate of 40% per day.
(a) Find the expected number of people who are newly infected on the 7th day.
(b) Find the expected number of infected people on the island after one whole week, assuming no one has recovered.
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