Starter quiz
Which type of sequence is represented by this graph?- arithmetic ✓
- geometric
- linear ✓
- non-linear
- quadratic
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- How can you tell that the sequence 17, 24, 31, 38, 45, ... is arithmetic?
- It is increasing.
- It has no negative terms.
- It has a common additive difference between successive terms. ✓
- It has a constant multiplicative relationship between successive terms.
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- How can you tell that the sequence 0.02, 0.2, 2, 20, 200, ... is geometric?
- It is increasing.
- It has no negative terms.
- It has a common additive difference between successive terms.
- It has a constant multiplicative relationship between successive terms. ✓
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Sofia plots the graph of this arithmetic sequence. Which of these coordinates should Sofia plot?- (1, 21) ✓
- (21, 1)
- (18, 15)
- (3, 15) ✓
- (18, 2)
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- Which of these will be one of the first five terms in the geometric sequence that has a first term of 1.25 and a common ratio of 2?
- 0.625
- 2.5 ✓
- 3.25
- 10 ✓
- 20 ✓
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The missing term of this geometric sequence is ______.- '96000' ✓
Exit quiz
This graph of (term number) against (term value) could represent which of these types of sequences?- linear
- geometric ✓
- arithmetic
- additive
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Jacob plots the graph of this geometric sequence. Which coordinates should Jacob plot?- (30, 150)
- (30, 2)
- (2, 30) ✓
- (750, 4)
- (4, 750) ✓
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How do you know that this graph might represent a geometric sequence?- The points form a straight line.
- The graph is increasing.
- The terms are all positive.
- The points form a curve. ✓
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- What do you know about the common ratio of this geometric sequence?
- It is positive.
- It is negative.
- It is large.
- It is less than 1.
- It is greater than 1. ✓
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Which of the below could be the ratio of this geometric sequence?-
- ✓
- ✓
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-
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You can draw a line through the points of this geometric sequence because it is modelling data that is ...- constant
- continuous ✓
- discrete
- rapidly increasing
- unknown
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Worksheet
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Presentation
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Lesson Details
Key learning points
- A geometric sequence looks like a curve when sketched (common ratio > 1 or < 1).
- The gradient increases sharply (common ratio > 1 or < 1).
- Although the graph is continuous, the sequence is not.
- Each geometric sequence is made up of discrete terms.
Common misconception
Pupils may thing that given the graph is continuous, the sequence can contain all of the values represented by the line.
It is important that pupils know when it is appropriate to draw a line to graph sequences and whether values on the line have any meaning. Sequences are often given as a list of terms and without context we cannot assume the sequence is continuous.
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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