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Lesson 1 of 9

Checking and securing understanding of non-linear sequences

I can appreciate that not all sequences are linear.

View unit
Lesson 1 of 9
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Checking and securing understanding of non-linear sequences

I can appreciate that not all sequences are linear.

Lesson details

Key learning points

  1. You can identify different types of sequences.
  2. If there is a common difference, the sequence is arithmetic.
  3. If there is a common ratio, the sequence is geometric.
  4. Special sequences will have different rules.

Keywords

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

  • Geometric sequence - A geometric sequence is a sequence with a constant multiplicative relationship between successive terms.

Common misconception

All sequences have to be arithmetic (linear) or geometric.

There are many types of sequences; arithmetic and geometric are just two types.

Make sure that pupils see a wide variety of sequences within the lesson and make sure they use precise language to describe any given sequence. It is also useful to get pupils to describe with precise language why a sequence like 5, 10, 20, 35, 55, ... is neither arithmetic nor geometric.
Teacher tip

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

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Prior knowledge starter quiz

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6 Questions

Q1.
The sequence -7, -3, 1, 5, 9, ... has a common difference of +4 therefore it is called __________ sequence.

Correct answer: an arithmetic
a counting
a geometric

Q2.
The sequence 4, 12, 36, 108, ...has a common ratio of ×4 therefore it is called __________ sequence.

an arithmetic
Correct answer: a geometric
a multiplier
a multiplier

Q3.
Match each arithmetic sequence to its next term.

Correct Answer:3, 5, 7, 9, 11, ...,13

13

Correct Answer:27, 24, 21, 18, 15, ...,12

12

Correct Answer:-19, -13, -7, -1, 5, ...,11

11

Correct Answer:-10, -6, -2, 2, 6, ...,10

10

Q4.
The next term of this geometric sequence 5, 15, 45, 135, ... is .

Correct Answer: 405

Q5.
Why is 50, 45, 39, 32, 44, ... not an arithmetic sequence?

Arithmetic sequences can not decrease.
It is an arithmetic sequence. The differences go -5, -6, -7, -8, ...
Correct answer: It does not have a common difference between terms.

Q6.
Which of these words describes the sequence -86, -74, -62, -50, ... ?

Correct answer: Additive
Correct answer: Arithmetic
Decreasing
Geometric
Correct answer: Linear

Assessment exit quiz

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6 Questions

Q1.
A sequence with a multiplicative, term-to-term relationship is called __________ sequence.

an arithmetic
Correct answer: a geometric
a linear
a multiplier

Q2.
Match the sequence to the descriptor.

Correct Answer:4, 8, 12, 16, ...,Arithmetic sequence

Arithmetic sequence

Correct Answer:2, 4, 8, 16, ...,Geometric sequence

Geometric sequence

Correct Answer:1, 4, 8, 13, ...,Other sequence

Other sequence

Q3.
Find the common ratio of the geometric sequence 192, 48, 12, ...

$$4$$
$$0.4$$
Correct answer: $$1\over4$$
$$2$$
$$1\over2$$

Q4.
What is the common second difference of the sequence 3, 12, 27, 48, ... ?

4
Correct answer: 6
9
15

Q5.
Select the statements that are true of the sequence 2, 16, 54, 128, 250, ...

It is geometric. It has a common ratio.
It is arithmetic. It has a common first difference between terms.
It has a common second difference.
Correct answer: It has a common third difference.
It has a common fourth difference.

Q6.
Which of these sequences will not always decrease?

1240, 620, 310, 155, ...
62, 51, 40, 29, ...
Correct answer: 104, 90, 80, 74, ...

Lesson appears in

UnitMaths / Graphical representations

Maths

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