Language of Sequences & Series (Cambridge (CIE) AS Maths): Revision Note
Exam code: 9709
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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 Sn to refer to the sum of the first n terms in the progression
ie. Sn = u1 + u2 + u3 + … + un

Increasing, decreasing and periodic progressions
A progression is increasing if un+1 > un for all positive integers n – ie if every term is greater than the term before it
A progression is decreasing if un+1 < un 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

Examiner Tips and Tricks
Look out for progressions defined by trigonometric functions – this can be a way of 'hiding' a periodic function.

Worked Example

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