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Checking and securing understanding of special number sequences

Lesson details

Learning outcome

I can identify the features of special number sequences.

Key learning points

  1. Special number sequences are not arithmetic.
  2. Special number sequences are not geometric.
  3. Special number sequences are generated using different rules.

Keywords

  • Square number - A square number is the product of two repeated integers.

  • Cube number - A cube number is the product of three repeated integers.

  • Triangular number - A triangular number (or triangle number) is a number that can be represented by a pattern of dots arranged into an equilateral triangle.

  • Sequence - A sequence is an ordered list of terms, usually formed according to a rule.

  • Nth term - The nth term of a sequence is the position of a term in a sequence where n stands for the term number.

Common misconception

After becoming very familiar with arithmetic sequences pupils can find the difference between the first two terms and just assume the sequence is arithmetic.

Pupils should check the relationship between all stated consecutive terms as they now have seen a variety of sequences.

Teacher tip

Encourage pupils to talk about how they think a sequence is continuing and how they can spot the different types of sequences. Sometimes working systematically and looking at differences between terms can help pupils spot the pattern.

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

6 Questions

Q1.
Which of these are square numbers?

Correct answer: 1
12
30
Correct answer: 64
94

Q2.
Which of these are cube numbers?

2
3
Correct answer: 8
16
Correct answer: 27

Q3.
Which of these are triangular numbers?

Correct answer: 3
Correct answer: 6
9
12
Correct answer: 15

Q4.
Which of these could be the first 4 terms of a sequence with term-to-term rule "add $$-3$$"

-3, 0, 3, 6, ...
Correct answer: 8, 5, 2, -1, ...
3, -3, -6, -9, ...
-11, -8, -5, -2, ...

Q5.
Which of these could be the first 4 terms in an arithmetic (linear) sequence?

5, 10, 20, 40, ...
-8, -5, 5, 8, ...
Correct answer: 3, 7, 11, 15, ...
10, 8, 6, 2, ...

Q6.
Which of these could be the first 4 terms in a geometric sequence?

Correct answer: 1, 2, 4, 8, ...
3, 6, 9, 12, ...
8, 4, 2, 0, ...
5, 6, 8, 11, ...
10, 12, 14, 16, ...

6 Questions

Q1.
The square numbers in ascending order can form a sequence with common difference. This means they form a quadratic sequence.

Correct Answer: second, 2nd

Q2.
What is the missing term in this sequence of all triangular numbers? 1, 3, 6, , 15, ...

Correct Answer: 10, ten

Q3.
Match the quadratic sequences to their common second differences.

Correct Answer:1, 3, 6, 10, 15, ...,common second difference of 1

common second difference of 1

Correct Answer:1, 4, 9, 16, 25, ...,common second difference of 2

common second difference of 2

Correct Answer:2, 8, 18, 32, 50, ...,common second difference of 4

common second difference of 4

Correct Answer:10, 30, 60, 100, 150, ...,common second difference of 10

common second difference of 10

Correct Answer:3, 9, 18, 30, ...,common second difference of 3

common second difference of 3

Q4.
If the $$15^\text{th}$$ square number is 225 and the $$16^\text{th}$$ square number is 256, what is the $$17^\text{th}$$ square number?

Correct Answer: 289

Q5.
If the $$15^\text{th}$$ triangular number is 120 and the $$16^\text{th}$$ triangular number is 136, what is the $$17^\text{th}$$ triangular number?

Correct Answer: 153

Q6.
Match these sequences up with their descriptions. They are all related to either the triangular, square or cube numbers.

Correct Answer:3, 10, 29, 66, ...,The cube numbers add 2

The cube numbers add 2

Correct Answer:3, 12, 27, 48, ...,The square numbers multiplied by 3

The square numbers multiplied by 3

Correct Answer:5, 12, 31, 68, ...,The cube numbers add 4

The cube numbers add 4

Correct Answer:5, 15, 30, 50, ...,The triangular numbers multiplied by 5

The triangular numbers multiplied by 5

Correct Answer:5, 20, 45, 80, ...,The square numbers multiplied by 5

The square numbers multiplied by 5


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