Formulas for Series: Connect Patterns with Math Equation

[mubashirmansoor]

I'd be glad if someone would provide me the ways or formulaes to connect a certain type of pattern through a mathmatical equation.

The simple ones are enough too.

Thankyou.

 

[Curious3141]

The question is way too general, what are you looking for ?

 

[arildno]

Your question is far too vague to be answerable.
Besides, use either formulae or formulas.

 

[mubashirmansoor]

What I mean is actually any method or a formulae for conecting a pattern, as an example ; 1,2,4,7,11... any method to connect these numbers by a certain formulae?

 

[Zurtex]

What I mean is actually any method or a formulae for conecting a pattern, as an example ; 1,2,4,7,11... any method to connect these numbers by a certain formulae?

Try this:

f(x) = 1  if  x = 1
       2  if  x = 2
       4  if  x = 3
       7  if  x = 4
       11 if  x = 5

Other than that, I think you are looking for this website:

http://www.research.att.com/~njas/sequences/

 

[dav2008]

You can define it recusively as

$$\left\{\begin{array}{l}a_0=1\\a_n=n_{n-1}+n\end{array}\right.$$

 

[mubashirmansoor]

Thankyou dav but I'm looking for an overall method

 

[BSMSMSTMSPHD]

Well, the "first differences" are 1,2,3,4, ... The "second differences" are 1,1,1,1, ... In other words, the second derivative is constant.

So, what kind of function has a constant second derivative?

Once you get this, it's pretty quick for any sequence of this type. I'll let you figure it out, since this smells like homework.

 

[HallsofIvy]

The only thing I can think of that is close to what you appear to want is "Newton's Divided Difference" interpolation formula. It can be used to find a polynomial that will give any finite sequence of values for n= 0, 1, 2, etc.
Look at
http://www.maths.lancs.ac.uk/~gilbert/m243a/node6.html

 

[mubashirmansoor]

Thankyou Bsmsmstmsphd but it's not the homework, I'm preparing for O'level matmatics exams so I need the method... thankyou

 

[HallsofIvy]

Then, unfortunately for you, there is no single "method" for determining the general term of a sequence from some of its values. In fact, given any finite number of terms there exist an infinite number of different sequences taking on those values.

If "the simplest polynomial formula" is sufficient then Lagranges' formula or (equivalently) Newton's divided difference formula would work.