Language of Sequences & Series (Cambridge (CIE) AS Maths) : Revision Note

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 + u₂ + u₃ + … + u_n

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