When should a situation be modelled with an arithmetic sequence rather than a geometric one?

When a fixed amount is repeatedly added or subtracted. A fixed percentage , or repeated multiplication by a fixed number, calls for a geometric model instead.

What feature of a real situation tells you a sequence or series model will fit?

A quantity changing by the same amount, or the same proportion, at regular intervals . Savings, salaries, commission and repeated depreciation all have exactly that shape.

A LevelMathsEdexcelPureFlashcardsSequences & SeriesModelling with Sequences & Series

Modelling with Sequences & Series (Edexcel A Level Maths: Pure): Flashcards

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FrontModelling with Sequences & Series
When should a situation be modelled with an arithmetic sequence rather than a geometric one?

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Cards in this collection (5)

When should a situation be modelled with an arithmetic sequence rather than a geometric one?
When a fixed amount is repeatedly added or subtracted.
A fixed percentage, or repeated multiplication by a fixed number, calls for a geometric model instead.
A salary rising by $\pounds 1500$ each year is $______$ ; a salary rising by $3 %$ each year is $______$ .
A salary rising by $\pounds 1500$ each year is arithmetic; a salary rising by $3 %$ each year is geometric.
A percentage rise multiplies the previous salary, so the increase itself grows each year.
In a savings problem, what is the difference between using the sequence and using the series?
The sequence gives the amount at a single point, such as the payment made in year $8$ .
The series gives the running total, such as everything paid in over the first $8$ years.
True or False?
Compound interest is modelled by a geometric sequence.
True.
Each year the amount is multiplied by the same factor, such as $1.03$ for $3 %$ interest.
The balance after $n$ years is therefore a term of a geometric sequence.
What feature of a real situation tells you a sequence or series model will fit?
A quantity changing by the same amount, or the same proportion, at regular intervals.
Savings, salaries, commission and repeated depreciation all have exactly that shape.

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