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

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.
$7.2 - 3.6 = 3.6$

$1.8 \ne 3.6$ So it is not an arithmetic progression.

Examining if it has a ratio:
We divide $2$ consecutive terms :
$\frac{3.6}{1.8} = 2$

Now we divide 2 more consecutive terms, to find out if all consecutive terms have the same ratio.
$\frac{7.2}{3.6} = 2$

$2 = 2$ 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:

$28.8 \cdot 2 = 57.6$
$57.6 \cdot 2 = 115.2$
$115.2 \cdot 2 = 230.4$

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