Expert: Steve Holleran - 1/5/2008

Question
Hi, first of all I just wanted to know if the Fibonacii Sequence is a function? I was thinking that it was becuase when put on a graph with (tn=yaxis n=xaxis) it passes the vertical line test. Is it a function?

Secondly I was having trouble with a question where I am given         (t1)= 1/2 ; (tn)= 1/2 x (t(n-1))
I am supposed to find an explicit formula for that equation. So, what I did was  find that it was geometric and used the equation tn=ar*n-1   (* means to the power of) where the (a is t1) a=1/2  and (r is the common difference) r= 1/2.  so I came up with   tn = 1/2 x 1/2*n-1    but the answer is supposed to be tn= 1/2*n what did I do wrong.

Answer
Hi Roshan,

First of all, yes, all sequences are functions with a domain of the counting numbers.

Secondly, you didn't do anything wrong.  If you take your result,
  
                 t(n) = 1/2 * (1/2)^(n-1)

and multiply the 1/2 's , you have

    t(n) = (1/2)^1 * (1/2)^(n-1) = (1/2)^(1 + n-1) or

                 t(n) = (1/2)^n.

Good work.

Steve