Language of Sequences & Series (Cambridge International A-Level Mathematics)

Language of sequences & series

What is a progression (sequence)?

• A progression (or sequence) is an ordered set of numbers with a rule for finding all the numbers in the progression

• The numbers in a sequence are called terms
• The terms of a progression are often referred to by letters with a subscript

What is a series?

• You get a series by summing up the terms in a progression

• We use the notation S_n to refer to the sum of the first n terms in the progression ie. S_n = u₁+ u ₂ + u₃ + … + u_n

What are increasing, decreasing and periodic progressions?

• A progression 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 progression 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 progression is periodic if the terms repeat in a cycle
• The order (or period) of a periodic progression is the number of terms in each repeating cycle

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

Worked Example