Starter quiz
- The sequence -7, -3, 1, 5, 9, ... has a common difference of +4 therefore it is called __________ sequence.
- an arithmetic ✓
- a counting
- a geometric
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- The sequence 4, 12, 36, 108, ...has a common ratio of ×4 therefore it is called __________ sequence.
- an arithmetic
- a geometric ✓
- a multiplier
- a multiplier
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- Match each arithmetic sequence to its next term.
- 3, 5, 7, 9, 11, ...⇔13 ✓
- 27, 24, 21, 18, 15, ...⇔12 ✓
- -19, -13, -7, -1, 5, ...⇔11 ✓
- -10, -6, -2, 2, 6, ...⇔10 ✓
- The next term of this geometric sequence 5, 15, 45, 135, ... is ______.
- '405' ✓
- Why is 50, 45, 39, 32, 44, ... not an arithmetic sequence?
- Arithmetic sequences can not decrease.
- It is an arithmetic sequence. The differences go -5, -6, -7, -8, ...
- It does not have a common difference between terms. ✓
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- Which of these words describes the sequence -86, -74, -62, -50, ... ?
- Additive ✓
- Arithmetic ✓
- Decreasing
- Geometric
- Linear ✓
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Exit quiz
- A sequence with a multiplicative, term-to-term relationship is called __________ sequence.
- an arithmetic
- a geometric ✓
- a linear
- a multiplier
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- Match the sequence to the descriptor.
- 4, 8, 12, 16, ...⇔Arithmetic sequence ✓
- 2, 4, 8, 16, ...⇔Geometric sequence ✓
- 1, 4, 8, 13, ...⇔Other sequence ✓
- Find the common ratio of the geometric sequence 192, 48, 12, ...
-
-
- ✓
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-
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- What is the common second difference of the sequence 3, 12, 27, 48, ... ?
- 4
- 6 ✓
- 9
- 15
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- Select the statements that are true of the sequence 2, 16, 54, 128, 250, ...
- It is geometric. It has a common ratio.
- It is arithmetic. It has a common first difference between terms.
- It has a common second difference.
- It has a common third difference. ✓
- It has a common fourth difference.
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- Which of these sequences will not always decrease?
- 1240, 620, 310, 155, ...
- 62, 51, 40, 29, ...
- 104, 90, 80, 74, ... ✓
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Worksheet
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Presentation
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Lesson Details
Key learning points
- You can identify different types of sequences.
- If there is a common difference, the sequence is arithmetic.
- If there is a common ratio, the sequence is geometric.
- Special sequences will have different rules.
Common misconception
All sequences have to be arithmetic (linear) or geometric.
There are many types of sequences; arithmetic and geometric are just two types.
Keywords
Arithmetic sequence - An arithmetic (or linear) sequence is a sequence where the difference between successive terms is a constant.
Geometric sequence - A geometric sequence is a sequence with a constant multiplicative relationship between successive terms.
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