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Sequences

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A sequence of numbers is a string of values which all have a pattern from one number to the next. Sequences come in many forms and you need to know how to find patterns and also describe them.

An example of a sequence is:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, etc.

In this sequence you add 2 to the previous number or multiply the position of the number by 2 (i.e. 1^st number = 1 × 2 and the 10^th number = 10 × 2).

Sequences can be defined in two ways:

• An Inductive Definision

This describes the pattern using the previous number in the sequence. You need a number to start you off.

An example is: u_n+1 = u_n + 5 if u₁ = 1
The sequence is - 1, 6, 11, 16, 21, 26, etc.

• An Iteration

An iteration creates a sequence by using the position of the number. To find the first number you put 1 into the formula and to find the second number you put 2 into the formula.

An example is: u_n = 2n + 1
The sequence is - 3, 5, 7, 9, 11, 13, etc.

There are several types of sequences:

• An arithmetic progression has an added fixed number
• A geometric progression have terms multiplied by a fixed number
• If a sequence gets closer to a number all the time it is convergent
• If a sequence gets further away from a number is is divergent

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by: Admin
Total views: 759
Word Count: 267
Date: Thu, 14 Sep 2006 Time: 12:00 AM
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Revision notes by Richard Tang

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