A question

A random person:

:| How to get the general formula of the set of numbers if there is a difference in two consecutive differences

I have trouble understanding your question but I think I'll give it a try.

Suppose difference 1 is given by the absolute value of a-b (so the value is a-b if a>b and b-a if a<b) and difference 2 is given by the absolute value of c-d.
Then the difference between the two differences is simply abs(abs(a-b)-abs(c-d)) [abs := absolute value]

To get the absolute value of for example x, one can also do the following; sqrt(x ²) [sqrt := square-root]

This would make the general formula for the set of numbers sqrt(sqrt((a-b) ²)-sqrt((c-d) ²))

I must however say that I find it a strange thing to make a general formula for, so perhaps I misinterpreted the question.

Perhaps you can give me an example to illustrate what you mean.


Reinout

A random person:

:| How to get the general formula of the set of numbers if there is a difference in two consecutive differences

I think this question might refer to number sequences. So, in a linear sequence where the differences are constant the n’th term is given by d.n + a – d where d is the difference and a is the first term.

I think you might be asking about quadratic sequences where the differences are changing but the second differences are constant. Here the n’th term is given by a + (n-1).d + (1/2).(n-1).(n-2).c where c is the difference between the differences and d is the difference between the first two numbers.

Hi random person,

Can you give us a concrete example of the type of sequence you are refering to please.
You have a captive audience here.