New
New
Year 8

# Representing sequences graphically

I can represent arithmetic sequences graphically and appreciate the common structure.

New
New
Year 8

# Representing sequences graphically

I can represent arithmetic sequences graphically and appreciate the common structure.

## Lesson details

### Key learning points

1. The terms in a sequence can be written as coordinates.
2. The coordinates can be plotted on a grid.
3. Arithmetic sequences have common structures.
4. Other sequences might have common structures you can investigate.

### Common misconception

When plotting sequences, a line must be drawn through the points.

Plot (1,5), (2,10), (3,15), draw a line and find other coordinates. When n = 1.5 the term value is 7.5. Is 7.5 in the sequence 5n??

### Keywords

• Arithmetic sequence - An arithmetic (or linear) sequence is a sequence where the difference between successive terms is a constant.

Learning cycle 2 sees students looking at the structure of an arithmetic sequence using bricks made up of dots. At this stage ask them to make up a picture of their own sequence and see if they can identify each others' sequences.
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).

## Starter quiz

### 6 Questions

Q1.
An arithmetic (linear) sequence has a __________ difference.
variable
unknown
positive
Q2.
Which two pairs of coordinates are shown here?
\$\$(1,2)\$\$ and \$\$(2,4)\$\$
\$\$(1,2)\$\$ and \$\$(4,2)\$\$
\$\$(2,1)\$\$ and \$\$(2,4)\$\$
Q3.
Match the letters with the correctly plotted coordinates.

\$\$(1,4)\$\$

\$\$(4,1)\$\$

\$\$(4,-1)\$\$

\$\$(1,-4)\$\$

Q4.
Which of these are true for this sequence?
When \$\$n=5, T=2\$\$
When \$\$n=5, T=5\$\$
Q5.
Match the sequences with the common difference.
Correct Answer:1, 8, 15, 22, ...,+7

+7

Correct Answer:1, -6, -13, -20, ...,-7

-7

Correct Answer:36, 30, 24, 18, ...,-6

-6

Correct Answer:-39, -33, -27, -21, ...,+6

+6

Correct Answer:0, 3, 7, 12, ...,No common difference

No common difference

Correct Answer:-17, -9, -1, 7, ...,+8

+8

Q6.
What is true of this set of coordinates?
The \$\$x\$\$ coordinate is always double the \$\$y\$\$ coordinate.
Correct answer: The \$\$y\$\$ coordinate is always double the \$\$x\$\$ coordinate.
The \$\$y\$\$ coordinate is always two more than the \$\$x\$\$ coordinate.
Correct answer: As the \$\$x\$\$ coordinate increases by 1, \$\$y\$\$ increases by 2

## Exit quiz

### 6 Questions

Q1.
When you plot an arithmetic sequence graphically the coordinates form a straight line, hence they are also known as __________ sequences.
straight
common difference
Q2.
If you completed this table of values before plotting the arithmetic sequence \$\$2n-7\$\$ which values would you put in the 'Term value' places?
Correct answer: -5, -3, -1, 1, 3
-2, 5, 12, 19, 26
-7, -5, -3, -1, 1
-7, -9, -11, -13, -15
-5, -7, -9, -11, -13
Q3.
This is a table of values for the sequence \$\$4n-11\$\$. If you were going to graph this sequence which of these coordinates are correct?
(-3,2)
(5,4)
Q4.
Which sequence is represented by this graph?
\$\$4-3n\$\$
\$\$3n+4\$\$
\$\$-5+3n\$\$
Q5.
This structure represents which sequence?
\$\$3+5n\$\$