An interesting Formula

A(x(x+1)/2))+1 where a is a even number; x is any number from 1 to infinity.

This strikingly general, simple, formula subsumes all my previous formulas for finding the rules of series like 1, 5, 13, 25,41,61, and so on… with the exception of series that do not have difference ax where a >1.

I will reference my other posts below.

Some other interesting series

Another interesting series of numbers.

An interesting series of numbers.

This formula iterates the terms of series with difference of 2Ax. Difference of Ax can be done with a being odd. To clarify suppose we have the series 1,3,7,13,21,31, and so on… , we will then assign a starting term of one firstly. Next, we will take the differences of each two terms i.e (3-1), (7-3), and so on. Then, we will find what multiple of an even number or odd number. is (in this case it is two). Now, we know the A value in my formula. Finally, just plug in any number from 1 to infinity.