Sequences

A set of numbers arranged in a particular order#

The simplest sequence: sequence of natural numbers

e.g - (counting numbers)

1,2,3,4,5,6,7,8,9,10,11..................

Other simple sequences are:

2,4,6,8,10,12,14...... (even numbers)

1,3,5,7,9,11,13..........(odd numbers)

2,3,5,7,11,13,17........(prime numbers)

& many more

To continue a sequence, you need to recognise a pattern.

Consider; 2,5,8,11

we can see that each number in this sequence is 3 units greater than the previous number

In a sequence the terms occur in a particular sequence

There is a: 1st term

2nd term

3rd term and so on..........

The value of each term depends upon its position in that order

The letter 'n' is used for a natural number

so we can refer to the n'th' term of a sequence in the same way we refer to the 4th term, or the 8th term etc.

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EXAMPLE 1 *[2] - means squared

The nth term of a sequence is given by the formula:

(n-1)(n-1) bsc. (n-1)[2] [squared]

Give the first 2 term and the 8th of the sequence:

First term ; n = 1 ; (1-1)[2] ; 0

Second term ; n = 2 ; (2-1)[2] ; 1

Eighth term ; n = 8 ; (8-1)[2] ; 49

Content of the notes (2)