Language of Sequences & Series (Edexcel IAL Maths)

Spec point — 4.3

Language of sequences & series

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 S_n to refer to the sum of the first n terms in the series i.e. S_n = u₁+ u ₂ + u₃ + … + u_n

What are increasing, decreasing and periodic sequences?

• A sequence is increasing if u_n+1 > u_n for all positive integers n

  • i.e. if every term is greater than the term before it

• A sequence is decreasing if u_n+1 < u_n for all positive integers n

  • i.e. 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

Exam Hint Look out for sequences defined by trigonometric functions – this can be a way of 'hiding' a periodic function.

Worked Example