# What is the geometric sequence for #3, 6, 12, 24, ...#?

##### 1 Answer

The geometric sequence is

#### Explanation:

In a geometric sequence, the terms are separated by a common ratio

#a_n= r xx a_(n-1)" "=r^1a_(n-1)#

#color(white)(a_n)=r xx(r xx a_(n-2))" "=r^2a_(n-2)#

#color(white)(a_n)=r xx r xx (r xx a_(n-3))" "=r^3a_(n-3)#

#color(white)(a_n)=...#

#a_n=r^(n-1)xxa_(n-(n"-"1))" "=r^(n-1)a_1#

This is often written with the initial value

#a_n=ar^(n-1)#

For the sequence *ratio* of any two successive terms.

(That is, since

Using

#r=a_2/a_1=6/3=2# .

Thus, the common ratio is 2, the first term is 3, and so the formula for this geometric sequence is

#a_n=ar^(n-1)#

#color(white)(a_n)=3*2^(n-1)# .