Seeking some math help

[etalns]

Okay, I've got a question here.

I have the following question

4,_,_,_,1024

I need to make this a geometric sequence.

Now, for this question I know how to get the answer. But I've looked everywhere and I can't find a formula for how to do it, I was wondering if anyone knew the formula for a geometric sequence and could enlighten me.

 

[Haircut]

A geometric sequence is one where U(n+1) = k * U(n)

In the example you provided we have U(1) = 4 and U(5) = 1024.
We need to find U(2), U(3) and U(4) and by the definition above we must multiply by a constant each time.

U(n+1) = k * U(n),
U(n+2) = k * U(n+1)
thus U(n+2) = k*k * U(n)

So, we can get U(n+x) = k^x * U(n)

Using the values we have U(5) = k^4 * U(1)
U(5)/U(1) = 256 = k^4, so k = 256^(1/4) = 4.
Thus the sequence increases by a factor of 4 each time

4, 16, 64, 256, 1024.