Expression of Equation

Question

Find the next three terms for the pattern following : (-1276),(+425),(-142),(+47)

Simple pattern here....

Only pattern I can find is that, the odd number term goes up by 1134, and the even number term goes down by 378.

Could anyone find other pattern than this??

And is it possible to express this in expression or summation form?

Thanks.

Answer 1

Why it is (obviously) $$S_n=504n^3-4158n^2+10647n-8269$$

Answer 2

Up to sign

$$(1276-1):3=425,$$

$$(425-1):3=142,$$

and so on

Answer 3

Actually, any continuation sequence is viable: a finite number of terms do not uniquely define any sequence! This "problem" is one that many intelligence tests proffer. For my money, it is merely a demonstration of the test writer's inability to handle logic.