Starter quiz
- If a numerical sequence does not have a common additive difference then you can say it is ...
- linear
- negative
- non-linear ✓
- not arithmetic ✓
- quadratic
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- Which of these sequences are not arithmetic sequences?
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- ✓
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- ✓
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- What is the result when you multiply by four times? You can use a calculator.
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- ✓
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- Use your calculator to halve then find half of your result and then halve it again. The result is ______.
- '10' ✓
What number should be written in the box in these equivalent ratios? ______.- '162' ✓
What number should be written in the box in these equivalent ratios? ______.- '81' ✓
Exit quiz
- A geometric sequence is a sequence with a constant __________ relationship between successive terms.
- additive
- decreasing
- increasing
- multiplicative ✓
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- The next term in this geometric sequence 7, 14, 28, ... is ______.
- '56' ✓
- Which of these are geometric sequences?
- 3, 6, 9, 12, ...
- 3, 6, 12, 24, ... ✓
- 3, 6, 10, 15, ...
- 3, 9, 15, 21, ...
- 3, 9, 27, 81, ... ✓
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- Which of these numbers will be a term in the geometric sequence: "Start on 2 and use a common multiplier of 5"?
- 10 ✓
- 50 ✓
- 100
- 500
- 1250 ✓
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- Which of these numbers will be terms of the geometric sequence: "Start on and use a common multiplier of "?
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- ✓
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- ✓
- ✓
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- The term of a geometric sequence is not zero and the common ratio is negative. Which of these statements is true about this sequence?
- It decreases.
- It decreases but never reaches zero.
- The terms will oscillate between positive and negative. ✓
- All of the terms will be negative.
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Worksheet
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Presentation
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Lesson Details
Key learning points
- Arithmetic sequences are not the only type of sequence.
- In a geometric sequence, there is still a first term.
- Instead of a common difference, there is a common multiplier.
- This common multiplier is referred to as the common ratio.
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
Geometric sequence - A geometric sequence is a sequence with a constant multiplicative relationship between successive terms.
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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