Graphing special number sequences using technology | Maths

Starter quiz

Which of these are square numbers?

8

14

16 ✓

26

81 ✓
Which of these are cube numbers?

25

30

47

64 ✓

100
Which of these are triangular numbers?

10 ✓

16

22

55 ✓

66 ✓
Which of these is the $n^{\text{th}}$ term rule for the linear sequence 6, 10, 14, 18, ...?

$n+4$

$n+6$

$4n + 2$ ✓

$4n + 6$

$6n + 4$
Sam draws a graph of this geometric sequence. Which of these coordinates should Sam plot?

(1, 5)

(2, 15) ✓

(3, 1)

(3, 15)

(4, 375) ✓
Andeep plots the graph of the equation $y=3.4x-10$ . When the $y$ coordinate is $75$ , the $x$ coordinate is ______.

'25' ✓

Exit quiz

$The sequence with <Math>n^{th}</Math> term <Math>5.6n + 12</Math> is graphed in the diagram. Is 40 a term in the sequence?$

The sequence with $n^{th}$ term $5.6n + 12$ is graphed in the diagram. Is 40 a term in the sequence?

yes ✓

no
$The 4th term in the sequence <Math>3\times 5^{n-1}</Math> is <span class="blank">______</span>. Use Desmos or the diagram to help you.$

The 4th term in the sequence $3\times 5^{n-1}$ is ______. Use Desmos or the diagram to help you.

'375' ✓
$Is the number 654 in the sequence with <Math>n^{\text{th}}</Math> term rule <Math>n^3</Math>? Use Desmos or the diagram to help you.$

Is the number 654 in the sequence with $n^{\text{th}}$ term rule $n^3$ ? Use Desmos or the diagram to help you.

Yes, because the two graphs intersect.

Yes, because $\sqrt[3]654$ is an integer.

No, because the graphs do not intersect at an integer $x$ value. ✓

No, because 654 is not on the curve with equation $y = n^3$ .
Why does this diagram not represent the sequence of all square numbers in ascending order?

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.

Sequences start when $n$ is 1 so there should not be coordinates when $x<1$ . ✓
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?

The number 1 is in both sequences.

The number 20 is in both sequences.

The number 28 is in both sequences. ✓

The 6th term in both sequences is the same.

The 8th term in both sequences are the same. ✓
$Which is the correct <Math>n^{\text{th}}</Math> term rule for the geometric sequence which starts 1, 2, 4, 8, 16, ...?$

Which is the correct $n^{\text{th}}$ term rule for the geometric sequence which starts 1, 2, 4, 8, 16, ...?

$2^{n+1}$

$2^n$

$2^n-1$ ✓

Worksheet

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Lesson Details

Key learning points

Visual representations of a sequence can help with identification.
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.