Sequences (nth Term) Formulas?

[SexyFag]

Hello, I Was Looking around The Forums And I heard That There Were Formulas For Finding The Nth Term Forumla? Is This So?
The One I Find is, If There is The same Difference Between Numbers, then We can Apply THis Forumla
a+(n-2)2
So, Can Anybody Tell Me All The Formulas Please?
Would Be Greatly Appreciated

 

[student92]

formula for sequences with same difference is first term+(n-1) * first difference( ie the same difference between the sequence)
this is the same formula as you wrote above just wording changes.
if you use this formula in paper, try not to show it in the working because it is out of our syllabus.

 

[SexyFag]

And What About When The Difference Between The Sequences are Not Uniform?
Like
see, For
2, 4, 6, 8
we Can use
a+(n-1)d
However, for something like
2, 4, 7, 11
etc..?

 

[SexyFag]

BUMP ^_^

 

[haochen]

 

[nightrider95]

There is an easy way to find the formula for the second difference. Perhaps what I am going to tell you isn't mention anywhere in the textbooks so note it down and keep it safe for future generations! :O:

As for finding the formula for the sequence like this :- 2,4,7,11 etc....

It is this :- 0.5(n^2)-0.5n+1

(2nd difference of the sequence/2)x(n^2)-nth formula

First you will take (1/2)x(n^2) and then find the nth formula . For finding the nth formula first do this rough working.

The first term of this sequence is 1 and how is that? Since 2,4 has a first difference of 2 and 4,7 has a difference of 3 . The second difference of 2 and 3 is 1. That is why I took (1/2) in the formula for the second difference. If you subtract 1 from 2 , you will get the difference of 1st term and 2nd term which will give you the first term of this sequence which is 1. It is important that the first difference should be one before you start the working because these are second difference sequences. In the first difference type of sequences, they can start with any number. But in these you have to be careful! So whenever you are doing any questions of second difference , always see that any term you have has a first difference of 1!

Having explained that, I will now tell you how to find the nth formula. We know that Nth formula is An= a+(n-1)d

'a' is the first difference of the term. 'd' is the difference of the 2nd and the 1st term.

The working for this is nth term number - (2nd a/2)(nth term)^2 = whatever the answer is.

e.g 1) 1-(0.5)(1)^2 = 0.5
2) 2-(0.5)(2)^2= 0
3) 4-(0.5)(3)^2 = -1/2 d= 2nd term - 1st term or 3rd term - 2nd term
d= 0 - 0.5 = -0.5 a= 1/2

An = a+(n-1)(d)
An= 0.5+(n-1)(-0.5)
An= 1/2+1/2 - 0.5n
An= -1/2+1

Now you have found the nth formula. Add this into the one that I found earlier.

It will be 0.5(n^2)-0.5n+1

The sequence is 1,2,4,7,11,16


Happy day everyone!

 

[adeel94]

the formula for the nth term is, a+(n-1)d

'a' stands for the first number of the sequence

'd' stands for difference between the sequence

i gave u a solved one

hope this helps

 

[SexyFag]

Wow, That Was A Very Through Explanation nightrider

Sadly However, I Wasnt Able TO UNderstand

However, IF you dont mind, could you take a sample (hard) question from a 0580 Math past paper, and then while explaining show you solved it?

Would Be Appreciated =)