How do you find the next three terms of the sequence 1.8,3.6,7.2,14.4,28.8,...?

We know it is a sequence, but we do not know if it is a progression.

There are #2# types of progressions, arithmetic and geometric.

Arithmetic progressions have a common difference, while geometric have a ratio. To find out if a sequence is an arithmetic or a geometric progression, we examine if consecutive terms have the same common difference or ratio.

Examining if it has a common difference:

We subtract #2# consecutive terms :
#3.6-1.8=1.8#

Now we subtract 2 more consecutive terms, to find out if all consecutive terms have the same common difference.
#7.2-3.6=3.6#

#1.8!=3.6# So it is not an arithmetic progression.

Examining if it has a ratio:
We divide #2# consecutive terms :
#3.6/1.8=2#

Now we divide 2 more consecutive terms, to find out if all consecutive terms have the same ratio.
#7.2/3.6=2#

#2=2# So it is a geometric progression.

Now, to find the next #3# terms of the geometric progression, we just multiply the last term with the ratio. So we have:

#28.8*2=57.6#
#57.6*2=115.2#
#115.2*2=230.4#

So, the next #3# terms are : #57.6, 115.2, 230.4#