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IB DP Maths: AI SL復習筆記1.2.4 Applications of Sequences & Series

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年7月19日上午10:21

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

Exam 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,

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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

Exam 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 7^th?day.

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