free physics video tutorials for all

 

Coursework Notes - Number

 

Sequences

 

[ common difference sequences ][changing difference sequences]

 

 

Conventionally sequences have a first term or starting value, usually denoted by the letter 'a'.

 

The common difference 'd' is the difference between consecutive terms when the terms increase by a regular amount.

 

The difference change 'c' is the change between consecutive differences

 

The last term in a sequence of 'n' numbers is the nth term.

 

 

The general term is an expression in 'n' that can be used to calculate any term in the sequence.

 

 

'Common Difference' Sequences

 

The general term for term number 'n' , common diff. 'd' and first term 'a' is:

 

dn + (a - d)

 

e.g. : 4.....9.....14.....19.....24.....29.....

 

a = 4, d = 5

 

 

the nth term is dn + (a - d) = 5n + (4 - 5) = 5n - 1

 

n = 7 , 7th term is (5 x 7) - 1 = 34

 

 

------------------------------------------------------------------------------------------------------------

 

example #1 - Find the nth term in this sequence : 13, 20, 27, 34, 41, 48 ...

 

a = 13, d = 7

 

nth term = dn + (a - d) = 7n + (13 - 7) = 7n +6

 

------------------------------------------------------------------------------------------------------------

 

example #2 - Find the nth term in this sequence : 11, 19, 27, 35, 43, 51 ...

 

a = 11, d = 8

 

nth term = dn + (a - d) = 8n + (11 - 8) = 8n + 3

 

------------------------------------------------------------------------------------------------------------

 

example #3 - Find the nth term in this sequence : 9, 15, 21, 27, 33, 39 ...

 

a= 9, d= 6

 

nth term = dn + (a - d) = 6n + (9 - 6) = 6n + 3

 

------------------------------------------------------------------------------------------------------------

 

back to top

 

 

 

'Changing Difference' Sequences

 

The general term for term number 'n' , common diff. 'd' , first term 'a' and difference change 'c' is:

 

changing diff. sequence

 

 

 

Example #1 - find the nth term of 3, 8, 14, 21, 29 ........

 

Writing the series with increases below:

 

series #1

 

remembering that the nth term is given by:

 

changing diff. sequence

 

1st term, 'a' =3

 

first difference 'd' = 5

 

difference increase 'c' = 1

 

sequences #2

 

------------------------------------------------------------------------------------------------------------

 

back to top

 

 

 

Example #2 - find the nth term of 5, 7, 10, 14, 19 ........

 

Writing the series with increases below:

 

series #4

 

remembering that the nth term is given by:

 

changing diff. sequence

1st term, 'a' =5

 

first difference 'd' = 2

 

difference increase 'c' = 1

 

series #3

 

 

back to top

 

 

 

creative commons license

All downloads are covered by a Creative Commons License.
These are free to download and to share with others provided credit is shown.
Files cannot be altered in any way.
Under no circumstances is content to be used for commercial gain.

 

 

 

 

©copyright gcsemathstutor.com 2015 - All Rights Reserved