Sequences

[smcennan]

What is the next term in the following sequence? -1/2 , 1 , 1/6 , 1/13 , ...

Is there a formula which is appropriate for this sequence?

 

[mmm4444bot]

Posting Guidelines (Summary)

Welcome to our tutoring boards! :) This page summarizes the main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to...

www.freemathhelp.com

 

[Dr.Peterson]

What is the next term in the following sequence? -1/2 , 1 , 1/6 , 1/13 , ...

Is there a formula which is appropriate for this sequence?

There is no next term; the sequence hasn't been defined!

One can find various formulas that yield these four numbers, but there is no guarantee that any such formula is "correct", and that the next term they generate is appropriate to whatever source the sequence came from.

But one such formula can be seen by considering the reciprocals of the numbers ...

 

[Steven G]

Here is one that surely works.
a_n = (20/39)n^3 - (331/78)n^2 + (415/39)n - (289/39)

 

[Cubist]

And here's another one for trig fans ...
(29 + 4*sqrt(493)*cos(pi*(2*n + 5)/4 + atan(5/31)) - 55*cos(pi*n))/156

However there's a much simpler formula, see the hint at the end of post#3