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Lesson 10 of 12
  • Year 11
  • Higher

Checking and securing understanding of geometric sequences

I can recognise the features of a geometric sequence and continue it.

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View unit
Lesson 10 of 12
New
New
  • Year 11
  • Higher

Checking and securing understanding of geometric sequences

I can recognise the features of a geometric sequence and continue it.

Download all resources
Share activities with pupils

These resources will be removed by end of Summer Term 2025.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.

These resources were created for remote use during the pandemic and are not designed for classroom teaching.

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Lesson details

Key learning points

  1. Identifying a common ratio between each term can help us identify a geometric sequence.
  2. Divide each term by its previous consecutive term, if the results are all the same, this is the common ratio.
  3. If there is a common ratio, then the sequence is geometric.

Keywords

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

  • Common ratio - A common ratio is a key feature of a geometric sequence. The constant multiplier between successive terms is called the common ratio.

Common misconception

The common multiplier must be a positive integer for the sequence to be geometric.

The multiplier needs to be the same between consecutive terms but it can be any value. Examples of this can be seen in the lesson.


To help you plan your year 11 maths lesson on: Checking and securing understanding of geometric sequences, download all teaching resources for free and adapt to suit your pupils' needs...

Task A Q4 involves terms with root 2 and pi. If not appropriate, this question can be removed.
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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

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Prior knowledge starter quiz

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6 Questions

Q1.
$$32-21=11$$, $$43-32=11$$ and $$54-43=11$$ shows that there is __________ additive difference between successive terms in this sequence. $$21, 32, 43, 54, ...$$

Correct answer: a common
an increasing
a decreasing
a non-integer

Q2.
Which of these sequences are arithmetic?

Correct answer: $$2, 4, 6, 8, 10, ...$$
$$2, 4, 7, 10, 14, ...$$
$$2, 4, 8, 16, 32, ...$$
Correct answer: $$2, 5, 8, 11, 14, ...$$
$$2, -5, 8, -11, 14, ...$$

Q3.
Which of the below sequences matches the description "start at $$5$$ and add four"?

$$5,10,15,20,25, ...$$
$$4,9,14,19,24, ...$$
Correct answer: $$5,9,13,17,21, ...$$
$$4,8,12,16,20, ...$$
$$5,1,-3,-7,-11, ...$$

Q4.
By what do we have to multiply $$13$$ to get to $$234$$?

Correct Answer: 18

Q5.
Match the sequences to their descriptions.

Correct Answer:$$2,4,6,8,10, ...$$,'Start at $$2$$ and add $$2$$'

'Start at $$2$$ and add $$2$$'

Correct Answer:$$2,4,8,16,32, ...$$,'Start at $$2$$ and double each time'

'Start at $$2$$ and double each time'

Correct Answer:$$1,2,4,8,16, ...$$,'Start at $$1$$ and double each time'

'Start at $$1$$ and double each time'

Correct Answer:$$1,2,3,4,5, ...$$,'Start at $$1$$ and add $$1$$'

'Start at $$1$$ and add $$1$$'

Correct Answer:$$1,3,5,7,9, ...$$,'Start at $$1$$ and add $$2$$'

'Start at $$1$$ and add $$2$$'

Correct Answer:$$2,0,-2,-4,-6, ...$$,'Start at $$2$$ and add $$-2$$'

'Start at $$2$$ and add $$-2$$'

Q6.
What is the next term in this sequence? $$-5, 10, -20, 40,$$

Correct Answer: -80

Assessment exit quiz

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6 Questions

Q1.
Arithmetic (linear) sequences have a common additive difference between successive terms and geometric sequences have a common __________ difference between successive terms.

Correct answer: multiplicative
subtractive
doubling

Q2.
What is the term-to-term rule of this sequence? $$4, 12, 36, 108, ...$$

$$+8$$
$$+24$$
$$\times4$$
Correct answer: $$\times3$$
'Double'

Q3.
Which of these sequences are geometric?

Correct answer: $$3,9,27,81,243, ...$$
$$3,9,36,180,1080, ...$$
$$3,9,15,21,27, ...$$
$$3,9,21,39,63, ...$$
Correct answer: $$3,12,48,192,768, ...$$

Q4.
Which of these are terms in the geometric sequence which starts like this? $$1600, 400, 100, ...$$

$$50$$
Correct answer: $$25$$
Correct answer: $$25\over4$$
$$25\over8$$
Correct answer: $$25\over16$$

Q5.
What is the missing first term in this geometric sequence? $$, 91, 637, 4459, ...$$

Correct Answer: 13

Q6.
What could the missing term in this geometric sequence be? $$8,$$ ... $$,32$$

$$12$$
Correct answer: $$16$$
$$20$$
Correct answer: $$-16$$
$$24$$