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

1 Answer
Apr 5, 2018

57.6, 115.2, 230.4

Explanation:

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