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Year 9

Graphing special number sequences using technology

I can plot the graph of a special number sequence.

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New
New
Year 9

Graphing special number sequences using technology

I can plot the graph of a special number sequence.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. Visual representations of a sequence can help with identification.
  2. Special number sequences can produce interesting graphs.

Common misconception

Pupils may think that given a 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

  • Triangular number - A triangular number (or triangle number) is a number that can be represented by a pattern of dots arranged into a triangle.

Using graphing software can allow pupils to see how a sequence grows and pupils should be encourage to explore what happens when they vary values in the n^th term formula.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Video

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Starter quiz

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6 Questions

Q1.
Which of these are square numbers?
8
14
Correct answer: 16
26
Correct answer: 81
Q2.
Which of these are cube numbers?
25
30
47
Correct answer: 64
100
Q3.
Which of these are triangular numbers?
Correct answer: 10
16
22
Correct answer: 55
Correct answer: 66
Q4.
Which of these is the $$n^{\text{th}}$$ term rule for the linear sequence 6, 10, 14, 18, ...?
$$n+4$$
$$n+6$$
Correct answer: $$4n + 2$$
$$4n + 6$$
$$6n + 4$$
Q5.
Sam draws a graph of this geometric sequence. Which of these coordinates should Sam plot?
An image in a quiz
(1, 5)
Correct answer: (2, 15)
(3, 1)
(3, 15)
Correct answer: (4, 375)
Q6.
Andeep plots the graph of the equation $$y=3.4x-10$$. When the $$y$$ coordinate is $$75$$, the $$x$$ coordinate is .
Correct Answer: 25

Exit quiz

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6 Questions

Q1.
The sequence with $$n^{th}$$ term $$5.6n + 12$$ is graphed in the diagram. Is 40 a term in the sequence?
An image in a quiz
Correct answer: yes
no
Q2.
The 4th term in the sequence $$3\times 5^{n-1}$$ is . Use Desmos or the diagram to help you.
An image in a quiz
Correct Answer: 375
Q3.
Is the number 654 in the sequence with $$n^{\text{th}}$$ term rule $$n^3$$? Use Desmos or the diagram to help you.
An image in a quiz
Yes, because the two graphs intersect.
Yes, because $$\sqrt[3]654$$ is an integer.
Correct answer: No, because the graphs do not intersect at an integer $$x$$ value.
No, because 654 is not on the curve with equation $$y = n^3$$.
Q4.
Why does this diagram not represent the sequence of all square numbers in ascending order?
An image in a quiz
Correct answer: The sequence has integer term numbers so the curve should not be drawn.
This should be a linear graph not a curve.
The $$y$$ axis scale is double the scale on the $$x$$ axis.
The square numbers are not on the curve.
Correct answer: Sequences start when $$n$$ is 1 so there should not be coordinates when $$x<1$$.
Q5.
This graph shows the sequence of triangular numbers and the sequence $$4n +4$$ (the line and curve are drawn to help you). Which of these statements are true?
An image in a quiz
The number 1 is in both sequences.
The number 20 is in both sequences.
Correct answer: The number 28 is in both sequences.
The 6th term in both sequences is the same.
Correct answer: The 8th term in both sequences are the same.
Q6.
Which is the correct $$n^{\text{th}}$$ term rule for the geometric sequence which starts 1, 2, 4, 8, 16, ...?
An image in a quiz
$$2^{n+1}$$
$$2^n$$
Correct answer: $$2^n-1$$