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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.

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Lesson details

Key learning points

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

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.

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.


To help you plan your year 9 maths lesson on: Graphing special number sequences using technology, download all teaching resources for free and adapt to suit your pupils' needs...

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.
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Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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 nth 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=3.4x10. When the y coordinate is 75, the x coordinate is .
Correct Answer: 25

6 Questions

Q1.
The sequence with nth 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 3×5n1 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 nth term rule n3? Use Desmos or the diagram to help you.
An image in a quiz
Yes, because the two graphs intersect.
Yes, because 6354 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=n3.
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 nth term rule for the geometric sequence which starts 1, 2, 4, 8, 16, ...?
An image in a quiz
2n+1
2n
Correct answer: 2n1
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