How do you find the explicit formula for the following sequence 12,24,48,...?

Mar 22, 2016

$12. {\left(2\right)}^{n - 1}$

Explanation:

This is a geometric sequence

The standard sequence has terms

a,ar,$a {r}^{2} , a {r}^{3} , a {r}^{4} , \ldots \ldots \ldots \ldots \ldots \ldots \ldots . , a {r}^{n - 1}$

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

$r = {a}_{2} / {a}_{1} = {a}_{3} / {a}_{2} = \ldots \ldots \ldots \ldots = {a}^{n} / {a}^{n - 1}$

the nth term of the sequence is : $a {r}^{n - 1}$

For this sequence a = 12 , $r = \frac{24}{12} = \frac{48}{24} = 2$

the nth term formula is therefore : $12. {\left(2\right)}^{n - 1}$