A square number is the product of two repeated integers.

A cube number is the product of three repeated integers.

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

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

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

Checking and securing understanding of special number sequences

Maths

In the prior unit, pupils considered other types of graphs. In this unit, pupils consider different types of sequences such as Fibonacci and oscillating. Their knowledge is consolidated by linking all prior learning together.

Further sequences

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

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

Match the quadratic sequences to their common second differences. 

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? 

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? 

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

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

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

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

Starter Quiz