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5.2 Order of sequence :

Terms “in order", means that one is free to define what order it is! One can go forwards, backwards or they could alternate or any type of order required.

A Sequence is like a Set, but with the terms in order.

Example: {0, 1, 0, 1, 0, 1, ...} is the sequence of alternating 0s and 1s. The set would be just {0,1}

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5.3 Types of sequences:

  1. i) Finite sequences: A sequence defined only for positive integers up to a certain integer are called finite sequences.

Example: {1, 3, 5, 7} is the sequence of the first 4 odd numbers

  1. ii) Infinite sequences: If the sequence goes on forever it is called an infinite sequence

Example: {20, 25, 30, 35, 40, ...} is an example of infinite sequence

  1. iii) Arithmetic sequences: In a sequence when a number is increasing or decreasing in a constant amount from the previous number is said to be in arithmetic sequence.

Example: 1, 4, 7, 10, 13, 16, 19

This sequence has a difference of 3 between each number and the pattern is continued by adding 3 to the last number each time.

  1. iv) Geometric Sequence: A sequence in which the ratio between each term and the previous term is a constant ratio is known as geometric sequence.

Example: 3, 9, 27, 81, 243, 729, 2187

This sequence has a factor of 3 between each number.

  1. v) Recursive Sequence: A sequence in which a general term is defined as a function of one or more of the preceding terms. A sequence is typically defined recursively by giving the first term, and the formula for any term an+1 after the first term.

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