Question

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

Answer 1

`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`