PLEASE:: How does exponential growth relate to geometric progression?

Question

anonymous · Answer

$$f (x) = a \times r ^{x}$$ is the equation for exponential growth
$$a, ar, ar ^{2}, ar ^{3}...$$ is the expression for geometric progression

anonymous · Answer

what is changing in each term?

anonymous · Answer

I'm not sure, but it has something to do with the domain. This is an answer I got online but I don't understand: An exponential function f on the domain of natural 
numbers defines a geometric progression. The nth term of the progression is f(n).

anonymous · Answer

if you have an exponential function, say a simple example of 
$$f(x)=2^x$$ then if you look at the sequence 
$$a_n=f(n), n = 1,2,3,...$$ you will see a geometric progression.  in the example i wrote you will see 
$$2,2^2,2^3,2^4,...$$

anonymous · Answer

in the example of 
$$f(x)=a\times r^x$$ then if you put 
$$f(n)=b_n, n =0, 1,2,3,...$$ you will get the geometric progression 
$$a,ar, ar^2, ar^3, ar6^4,...$$

anonymous · Answer

type should be 
$$ar^4,...$$

anonymous · Answer

I still do not understand this. How did you get $$a _{n}$$ ?