What is a sequence?
- A sequence is an ordered set of numbers with a rule for finding all the numbers in the sequence
- The numbers in a sequence are called terms
- The terms of a sequence are often referred to by letters with a subscript
What is a series?
- You get a series by summing up the terms in a sequence
- We use the notation Sn to refer to the sum of the first n terms in the series
ie. Sn = u1 + u2 + u3 + … + un
Increasing, decreasing and periodic sequences
- A sequence is increasing if un+1 > un for all positive integers n – ie if every term is greater than the term before it
- A sequence is decreasing if un+1 < un for all positive integers n – ie if every term is less than the term before it
- A sequence is periodic if the terms repeat in a cycle
- The order (or period) of a periodic sequence is the number of terms in each repeating cycle
Look out for sequences defined by trigonometric functions – this can be a way of 'hiding' a periodic function.