Given the sequence 3, 6, 12, 24, ... calculate the 9th and the nth terms of the sequence .

First, we'll from ratios from 2 consecutive terms of the
given sequence:

6/3 = 2

12/6 =
2

24/12 = 2

We notice that all
quotients are the same, so, the sequence is a geometric progression, whose first terms
is a1 = 3 and the common ratio is r = 2.

We'll calculate
a9:

a9 = a1*r^(9-1)

a9 = 3 *
2^8

a9 
=3*256

a9 =
768

The standard formula for any term of a
geometric progression is:

an =
a1*r^(n-1)