# Coming up with recursive and closed form expressions

## Homework Statement

I am having some trouble coming up with recursive and closed form expressions of different sequences. I realize helping me with this would pretty much just be giving me the answer, but if anyone could also help me with how to think of the answers that would be nice.

1) Cn = (1/4, 1/12, 1/36, 1/108)

CF: ?
R: C(n-1)/3

2) Dn = (1, 2, 6, 24, 120)

CF: ?
R: n*D(n-1)

3) I only need the closed form for this. (1/3, 4/5, 7/7, 10/9, 13/11)

CF: ?/2n+1

4) Let (1, 1, 2, 3, 5, 8) be the Fibonacci sequence. Define a new sequence by Qn = F(n+1)/Fn

a. List the first several terms of Qn
(1, 2, 3/2, 5/3, 8/5)

b. Find a recusive formula for Qn

?

$C_0 = 1/4, C_n = C_{n - 1} / 3$
(note how I wrote down explicitly what $C_{n-1}/3$ gives you by using an equality sign, and that I have included the first term which you need to calculate anything using the recursion relation).