Revision Notes

2.10.1 Sequences - Linear

What is a sequence?

  • A sequence is simply a set of numbers (or objects) in an order

What is a linear sequence?

  • A linear sequence is one where the numbers go up (or down) by the same amount each time
    • eg 1, 4, 7, 10, 13, … (add 3 to get the next term)
    • 15, 10, 5, 0, -5, … (subtract 5 to get the next term)
  • If we look at the differences between the terms, we see that they are constant

What can we do with linear sequences?

  • You should be able to recognise and continue a linear sequence
  • You should also be able to find a formula for the nth term of a linear sequence in terms of n
  • This formula will be in the form:
    nth term = dn + b
    d is the common difference, b is a constant that makes the first term “work”

How to find the nth term formula for a linear sequence

  • Find the common difference between the terms – this is d
  • Put the first term and n=1 into the formula, then solve to find b

Worked Example

nth term (linear) Worked Example, downloadable IGCSE & GCSE Maths revision notes


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