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Use a Known GP Term to Find a Later Term

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Predicting What Comes Next: Exploring Sequences and Progressions · GP term applications · 3:31

You'll learn: Move a fixed number of positions by multiplying by the ratio that many times.

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Use a Known GP Term to Find a Later Term

3:31

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Use a Known GP Term to Find a Later Term

You'll learn: Move a fixed number of positions by multiplying by the ratio that many times.

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GP term applications

1

Which GP Term Equals a Given Number?
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Which GP Term Equals a Given Number?
You'll learn: Match the target with a power of the common ratio.

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Fractals and geometric patterns

6

Build the Sierpiński Triangle One Removal at a Time
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Build the Sierpiński Triangle One Removal at a Time
You'll learn: Join side midpoints and remove each central small triangle repeatedly.
Count the Small Triangles with a Power of Three
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Count the Small Triangles with a Power of Three
You'll learn: Explain why each retained triangle produces three at the next stage.
More Triangles Can Occupy Less Total Area
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More Triangles Can Occupy Less Total Area
You'll learn: Use the retained fraction to model the shrinking shaded area.
Plot AP and GP Behaviour Side by Side
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Plot AP and GP Behaviour Side by Side
You'll learn: Compare constant additive change with multiplicative growth and decay.
Build and Count a Sierpiński Square Carpet
3:41
Build and Count a Sierpiński Square Carpet
You'll learn: Remove the central ninth in every retained square and count the remaining pieces.
Find the Shrinking Area of the Square Carpet
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Find the Shrinking Area of the Square Carpet
You'll learn: Apply the retained fraction8/9 at every stage.

Next topic

Bouncing-ball applications

2

A Bouncing Ball’s Heights Form a Shrinking GP
3:50
A Bouncing Ball’s Heights Form a Shrinking GP
You'll learn: Generate bounce maxima and find the first bounce below a specified threshold.
Count Both Upward and Downward Travel Between Bounces
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Count Both Upward and Downward Travel Between Bounces
You'll learn: Distinguish rebound height from total vertical distance travelled.

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Chapter challenge problems

6

A Shifted Recursive Sequence Can Reveal a GP
3:28
A Shifted Recursive Sequence Can Reveal a GP
You'll learn: Transform the recurrence into a geometric rule and identify a target term.
Count Multiples Within a Fixed Number Range
3:46
Count Multiples Within a Fixed Number Range
You'll learn: Use the smallest and largest allowable multiples and the AP term formula.
Recover an AP from Sums of Two Terms
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Recover an AP from Sums of Two Terms
You'll learn: Convert term-sum information into two linear conditions on a and d.
When Does a Natural-Number Sum First Exceed One Thousand?
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When Does a Natural-Number Sum First Exceed One Thousand?
You'll learn: Use the triangular-sum formula and test neighbouring integer positions.
Write One Hundred as Consecutive Natural Numbers
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Write One Hundred as Consecutive Natural Numbers
You'll learn: Use a starting value and number ofterms to find every valid representation.
A Doubling Bacterial Culture Uses Stage Zero
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A Doubling Bacterial Culture Uses Stage Zero
You'll learn: Model the initial count and subsequent hourly doublings.