Square, cube and triangular numbers, Fibonacci-type sequences, and telling sequence types apart.
What you will learn
- Recognise square, cube and triangular numbers
- Work with Fibonacci-type sequences
- Say what type a sequence is
Sequences to know
- Square numbers 1, 4, 9, 16, ...: nth term n².
- Cube numbers 1, 8, 27, 64, ...: n³.
- Triangular numbers 1, 3, 6, 10, 15, ...: n(n + 1)/2 (the dots in a triangle).
- Fibonacci-type: each term is the sum of the two before. 1, 1, 2, 3, 5, 8, ... or 2, 5, 7, 12, 19, ...
- Powers of 2: 2, 4, 8, 16, ... doubles each time: nth term 2ⁿ, so the 10th term is 2¹⁰ = 1024.
A sequence close to the square numbers can be found by comparing: 4, 7, 12, 19, ... is 3 more than 1, 4, 9, 16, ..., so its nth term is n² + 3.
The types to recognise: arithmetic (linear) sequences add the same amount each time; geometric sequences multiply by the same number (lesson 4); quadratic sequences have a constant second difference (lesson 5); in Fibonacci-type sequences each term is the sum of the two before.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Sequences to know
- Unknown starting terms
7 practice questions, marked as you go; about 20 minutes in all.
Key terms
Arithmetic, Geometric, Quadratic, Fibonacci-type
In this unit: Sequences
Term-to-term rules, the nth term of linear sequences, special sequences, geometric sequences and (Higher) the nth term of quadratic sequences.