Language of Sequences & Series (AQA A Level Maths) : Revision Note

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

  ie.   S_n = u₁ + u₂ + u₃ + … + u_n

Increasing, decreasing and periodic sequences

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