Originally Posted by

**math-** hi everyone!

ok, i have an investigation where i must consider some fraction sequences.

first row- 1/2, 2/3, 3/4, 4/5 5/6, 6/7, 78

second row- 1/6, 1/12, 1/20, 1/30, 1/42, 1/56

third row- 1/12, 1/30, 1/60, 1/105, 1/168

fourth- 1/20, 1/60, 1/140, 1/280

...

Hello,

as Geometor suggested I'll use the denominators only:

Consider the following sequence and calculate the diffferences between the numbers: Code:

6 12 20 30 42 56
6 8 10 12 14
2 2 2 2

The differences of the differences yield a constant sequence. Thus your sequence is of the second grade/degree(?) and the general equation of such a sequence is:

You know

Solve this system of simultaneous equations. I've got: a = 1, b = 3, c = 2

That means the sequence have the equation

And the numbers in the second row can be calculated by:

If you apply this method to your 3rd row you'll get a sequence of third grade/degree(?). Thus you have to solve a system of 4 simultaneous equations:

Solve this system. I've got as the final result that the numbers in the third row can be calculated by: