techniques for finding an expression for geometric seqeunces

[rogermiranda]

I know that there are certain techniques and steps on finding expressions for linear and quadratic sequences. But can someone give me a technique or set of steps that I can use to figure out expressions for geometric sequences?
For example, I have the geometric sequence 4,8,16,32,64.... The common ratio is 2. The expression to generate this sequence is 2^n+1. But I would like to learn the steps needed to figure out the expression. Can someone please help.

[king&i]

They've got a lesson here: http://www.purplemath.com/modules/series3.htm

You can use the fomrulas. Like for 4,8,16,32,64, you have r=2, a=4. then a_n=a*2^n-1. And a=4=2², so a_n=(2²)(2^n-1)=2^2+n-1=2ⁿ⁺¹.