Let Rn be the number of dots in a rectangular array of dots with n columns and n+1 rows

Rn= n(n+1) so we get (1,2) (2,6) (3,12) (4,20) (5,30)

Determine if this sequence is arithmetic, geometric, or neither

this will be neither right because the difference between pairs is not constant. The difference from 2 to 6 and 6 to 12 is not the same so it cannot be arithmetric and 6/2 is not the same as 12/6 and so on thus this cannot be geometric

Is that correct thinking?

will all geometric sequences be a exponential curve?

This is a geometric sequence because the ratio is -3

r1=-4

rn=-3rn-1

so we get

(1,-4) (2,12) (3,-36) (4,108) ......

I do not understand how this is exponential because it alternates positive to negative I can say they are linear between points and when graphed if I was going to connect more of a sine graph