# How do you write an explicit formula for this sequence: 3, 6, 12, 24?

Mar 13, 2016

$3 . {2}^{n - 1}$

#### Explanation:

This is a geometric sequence , the standard sequence being :

$a , a r , a {r}^{2} , a {r}^{3} , \ldots \ldots \ldots \ldots \ldots \ldots . . , a {r}^{n - 1}$

where a , is the 1st term and r , the common ratio

here a = 3 and $r = \frac{6}{3} = \frac{12}{6} = \frac{24}{12} = 2$

to generate terms in the sequence use $a {r}^{n - 1}$

$\Rightarrow a {r}^{n - 1} = {3.2}^{n - 1}$

so 1st term n = 1 : ${3.2}^{1 - 1} = {3.2}^{0} = 3.1 = 3$

2nd term n= 2 : ${3.2}^{2 - 1} = {3.2}^{1} = 6$

4th term n=4 : ${3.2}^{4 - 1} = {3.2}^{3} = 3.8 = 24$