Starter quiz
- Which of these are square numbers?
- 1 ✓
- 12
- 30
- 64 ✓
- 94
-
- Which of these are cube numbers?
- 2
- 3
- 8 ✓
- 16
- 27 ✓
-
- Which of these are triangular numbers?
- 3 ✓
- 6 ✓
- 9
- 12
- 15 ✓
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- Which of these could be the first 4 terms of a sequence with term-to-term rule "add "
- -3, 0, 3, 6, ...
- 8, 5, 2, -1, ... ✓
- 3, -3, -6, -9, ...
- -11, -8, -5, -2, ...
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- Which of these could be the first 4 terms in an arithmetic (linear) sequence?
- 5, 10, 20, 40, ...
- -8, -5, 5, 8, ...
- 3, 7, 11, 15, ... ✓
- 10, 8, 6, 2, ...
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- Which of these could be the first 4 terms in a geometric sequence?
- 1, 2, 4, 8, ... ✓
- 3, 6, 9, 12, ...
- 8, 4, 2, 0, ...
- 5, 6, 8, 11, ...
- 10, 12, 14, 16, ...
-
Exit quiz
- The square numbers in ascending order can form a sequence with common ______ difference. This means they form a quadratic sequence.
- 'second' ✓
- What is the missing term in this sequence of all triangular numbers? 1, 3, 6, ______, 15, ...
- '10' ✓
- Match the quadratic sequences to their common second differences.
- 1, 3, 6, 10, 15, ...⇔common second difference of 1 ✓
- 1, 4, 9, 16, 25, ...⇔common second difference of 2 ✓
- 2, 8, 18, 32, 50, ...⇔common second difference of 4 ✓
- 10, 30, 60, 100, 150, ...⇔common second difference of 10 ✓
- 3, 9, 18, 30, ...⇔common second difference of 3 ✓
- If the square number is 225 and the square number is 256, what is the square number?
- '289' ✓
- If the triangular number is 120 and the triangular number is 136, what is the triangular number?
- '153' ✓
- Match these sequences up with their descriptions. They are all related to either the triangular, square or cube numbers.
- 3, 10, 29, 66, ...⇔The cube numbers add 2 ✓
- 3, 12, 27, 48, ...⇔The square numbers multiplied by 3 ✓
- 5, 12, 31, 68, ...⇔The cube numbers add 4 ✓
- 5, 15, 30, 50, ...⇔The triangular numbers multiplied by 5 ✓
- 5, 20, 45, 80, ...⇔The square numbers multiplied by 5 ✓
Worksheet
Presentation
Video
Lesson Details
Key learning points
- Special number sequences are not arithmetic.
- Special number sequences are not geometric.
- Special number sequences are generated using different rules.
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.
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.