sequences 2

The nth term is $a(n) = (n - 1)(n)(n + 1)$ , making

$a(7) = 6*7*8 = 336$ .

This expression can be simplified to $a(n) = n^{3} - n$ , equivalent to Sathish's observation.

1^3-1=0, 2^3-2=6, 3^3-3=24..........7^3-7=336 !!

I'm just playing with those numbers fortunately I got the right answer!

*Divide all numbers by six *

$0/6=0,6/6=1,24/6=4,60/6=10,120/6=20,210/6=35,z/6=y$

subtract the answers by descending order

$1-0=1,4-1=3,10-4=6,20-10=10,35-20=15,y-35=x$

subtract again the answers by descending order

$3-1=2,6-3=3,10-6=4,15-10=5,x-15=6$

Find the value of x so that the answers must be consecutive.

$x=21$

$y=56$

$z =336$