[Math] systematic way of resolving sequences of dots in figures

sequences-and-series

http://bibliotecadigital.ilce.edu.mx/sites/telesecundaria/tsm01g01v01/u02t04s01.html

enter image description here

I wonder if there is a systematic way to get the formula of a sequence of dots in figures, to resolve it faster, and apply it to other figures.

Thanks!

Best Answer

To the get the linear equation of type:

y=kx+b

In which, y is the number of total balls and x is the sequence element's number. If you have access to 2 elemnts and its corresponding number of balls simply solve this system of equations. For example, y(1)=6 and y(2)=10, then

| 6=k*1+b   <=>  |k=4
| 10=k*2+b       |b=2

So the final equation would be:

y=4x+2

If you wante to calculate element 50, replace x with that value and you have the total number of balls:

y=4*50+2=202

This is the same method applied when you know 2 dots in a linear graph.

Related Question