Starter quiz
- __________ sequence is a sequence with a constant multiplicative relationship between successive terms.
- An arithmetic
- A geometric ✓
- A multiplier
- A quadratic
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- In the geometric sequence 1.2, 4.8, 19.2, 76.8, ..., the common __________ between the terms is 4.
- difference
- multiplier ✓
- ratio ✓
- sequence
- term
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- Find the next two terms in this geometric sequence: 3, 30, 300, ...
- 330
- 600
- 3000 ✓
- 30 000 ✓
- 33 000
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- Which of these are terms in the geometric sequence generated by the rule: "Start on and use a common ratio of "?
- ✓
- ✓
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- ✓
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- Some of these sequences are geometric, some are arithmetic. Select all the geometric sequences.
- 1, 2, 3, 4, ...
- 1, 2, 4, 8, ... ✓
- 1000, 200, 40, 8, ... ✓
- 200, 80, -40, -160, ...
- 1, 3, 9, 27, ... ✓
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- Which statement is true of the sequence 1, 2, 6, 24, 120, ... ?
- It is geometric.
- It is arithmetic.
- It is geometric because the multipliers are: ×2, ×3, ×4, ×5
- It has no common ratio therefore it is not geometric. ✓
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Exit quiz
- The constant multiplier between successive terms in a geometric sequence is called the common ______.
- 'ratio' ✓
- The common ratio of the geometric sequence 7, 28, 112, 448, 1792, ... is ______.
- '4' ✓
- 312, 2184, 15 288, 107 016, 749 112, ... is a geometric sequence. Which of these divisions will give you the common ratio?
- ✓
-
- ✓
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-
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- Match each geometric sequence to its common ratio.
- 16, 80, 400, 2000, ...⇔5 ✓
- 4.2, 16.8, 67.2, 268.8, ...⇔4 ✓
- 0.07, 0.56, 4.48, 35.84, ...⇔8 ✓
- 1602, 4806, 14 418, 43 254, ...⇔3 ✓
- 20 376, 10 188, 5094, 2547, ...⇔✓
- 2, 0.4, 0.08, 0.016, ...⇔✓
The first term of this geometric sequence is ______.- '247' ✓
What could the third term of this geometric sequence be?- 20 ✓
- 25
- -20 ✓
- -25
- 80
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Worksheet
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Presentation
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Lesson Details
Key learning points
- Identifying a common ratio between each term can help us identify a geometric sequence.
- Divide each term by its previous consecutive term, if the results are all the same, this is the common ratio.
- If there is a common ratio, then the sequence is geometric.
Common misconception
After becoming very familiar with arithmetic sequences pupils can find the difference between the first two terms and just assume the sequence is arithmetic.
Explore a large number of geometric and arithmetic sequences and see if pupils can articulate how they check if a sequence is geometric. They might say the terms of the sequence grow more quickly (for some geometric sequences).
Keywords
Common ratio - A common ratio is a key feature of a geometric sequence. The constant multiplier between successive terms is called the common ratio.
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