# I Need An Equation

Qwerty
I have the following pattern and i need an equation that if x = 1 then y will equal the fist number of it, if x = 2, then y will equal the 2nd number.

The pattern is:
2, 4, 16, 256, 65536

Hint: It keeps squaring itself.

Any ideas?

NateTG
Homework Helper
Try writing all of them as powers of 2:
21,22,24,28,216

It should be easy from there...

Qwerty
Try writing all of them as powers of 2
But this doesnt help me much becasue it doesnt find my numbers i need in an equation...

f(x) = 2^2x

Last edited:
Qwerty
f(x) = 2^2x
I had already thought of this but it does not work...Here is teh pattern it gives you.
4,16,64,256
This is the pattern I want...
2, 4, 16, 256, 65536

There is not supposed to be 64 and it also skips 2

Originally posted by PrudensOptimus
f(x) = 2^2x
No, that gives 22, 24, 26, ...

I don't think we should be giving explicit formulas anyway, since it sounds like homework.

Qwerty, take NateTG's suggestion and first find a formula for just the exponents 1, 2, 4, 8, 16, ... from that you can derive a formula for the actual sequence.

it turns out to be quite a function with an even nicer derivative

Qwerty
I don't think we should be giving explicit formulas anyway, since it sounds like homework.
Acually no, it's not for homework....its for a project im working on(programming).

And I don't need your help anymore, I found the answer to my question myself.

MathematicalPhysicist
Gold Member
Originally posted by Qwerty
Acually no, it's not for homework....its for a project im working on(programming).

And I don't need your help anymore, I found the answer to my question myself.
Originally posted by Qwerty
I have the following pattern and i need an equation that if x = 1 then y will equal the fist number of it, if x = 2, then y will equal the 2nd number.

The pattern is:
2, 4, 16, 256, 65536

Hint: It keeps squaring itself.

Any ideas?
if you first put x=1 (as you requested) to this equation you get 2^(2^1)=4 which is not the first number 2 ofcourse.
but if you put first x=0 then this is the equation you were looking for this pattern.

Qwerty
if you first put x=1 (as you requested) to this equation you get 2^(2^1)=4 which is not the first number 2 ofcourse.
Yes this is an error in my first post, 0 is supposed to be the first number subsituted into the equation.