New
New
Year 9

Features of special number sequences

I can appreciate the features of special number sequences, such as square, triangular and cube.

New
New
Year 9

Features of special number sequences

I can appreciate the features of special number sequences, such as square, triangular and cube.

Lesson details

Key learning points

  1. Square number sequences are formed by squaring the position within the sequence.
  2. Cube number sequences are formed by cubing the position within the sequence.
  3. Triangular number sequences are formed by increasing the difference by one between each consecutive term.
  4. These special number sequences can be represented visually.

Common misconception

Square numbers are any number that can be squared.

Give students counters or let them draw dot patterns to explore square numbers geometrically as well as numerically.

Keywords

  • Triangular number - A triangular number is a number that can be represented by a pattern of dots arranged into an equilateral triangle. The term number is the number of dots in a side of the triangle

Explore the structure of these number sequences using counters if possible so that students can see how these special sequences are generated and can explore the link between triangular numbers and square numbers. Building cube numbers can also show students it's not just the number times 3.
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).

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6 Questions

Q1.
Which of these are square numbers?
Correct answer: 1
2
10
Correct answer: 49
Correct answer: 100
Q2.
Which of these arrays represent a square number?
An image in a quiz
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
Q3.
Which of these are cube numbers?
Correct answer: 1
3
9
16
Correct answer: 27
Q4.
Match each sequence with its term-to-term rule.
Correct Answer:4, 12, 36, 108, ...,multiply previous term by 3 to get the next term

multiply previous term by 3 to get the next term

Correct Answer:4, 12, 20, 28, ....,add 8 to the previous term to get the next term

add 8 to the previous term to get the next term

Correct Answer:4, 12, 22, 34, ...,add 8, then add 10, increasing the difference by 2 each time

add 8, then add 10, increasing the difference by 2 each time

Correct Answer:4, 12, 21, 31, ...,add 8, then add 9, increasing the difference by 1 each time

add 8, then add 9, increasing the difference by 1 each time

Correct Answer:4, 12, 28, 60, ... ,multiply the previous term by 2 and add 4 to get the next term

multiply the previous term by 2 and add 4 to get the next term

Q5.
Which of these could be a position-to-term rule for the sequence which starts 5, 8, 11, 14, 17, ... ?
add 3 to the term number
multiply the term number by 2 and add 3
multiply the term number by 3
Correct answer: multiply the term number by 3 and add 2
multiply the term number by 4
Q6.
Which of these could be the first 4 terms of a geometric sequence?
1, 4, 8, 16
Correct answer: 8, 12, 18, 27
5, 15, 25, 35
Correct answer: 125, 25, 5, 1
0.5, 1, 2, 3.5

6 Questions

Q1.
Starting with the smallest triangular number, order these numbers so they form the sequence of triangular numbers in ascending order.
1 - 1
2 - 3
3 - 6
4 - 10
5 - 15
6 - 21
Q2.
Which of these arrays correctly represents a triangular number?
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
Q3.
The $$n^{\text{th}}$$ term rule for a sequence is $$n^{2}$$. The $$8^{\text{th}}$$ term in the sequence is .
Correct Answer: 64, sixty four, sixty-four
Q4.
The $$13^{\text{th}}$$ triangular number is 91. The $$14^{\text{th}}$$ triangular number is .
Correct Answer: 105
Q5.
Match each answer to the correct calculation.
Correct Answer:24,$$4^{th}$$ square number + $$2^{nd}$$ cube number

$$4^{th}$$ square number + $$2^{nd}$$ cube number

Correct Answer:122,$$1^{st}$$ triangular number + $$11^{th}$$ square number

$$1^{st}$$ triangular number + $$11^{th}$$ square number

Correct Answer:100,$$9^{th}$$ triangular number + $$10^{th}$$ triangular number

$$9^{th}$$ triangular number + $$10^{th}$$ triangular number

Correct Answer:140,$$5^{th}$$ cube number + $$5^{th}$$ triangular number

$$5^{th}$$ cube number + $$5^{th}$$ triangular number

Correct Answer:8,$$6^{th}$$ square number − $$7^{th}$$ triangular number

$$6^{th}$$ square number − $$7^{th}$$ triangular number

Correct Answer:0,$$8^{th}$$ square number − $$4^{th}$$ cube number

$$8^{th}$$ square number − $$4^{th}$$ cube number

Q6.
The hexagonal numbers are made by arranging dots on hexagonal shapes. Using the diagram, the $$5^{\text{th}}$$ hexagonal number is .
An image in a quiz
Correct Answer: 45, forty five, forty-five