Find the nth term of the sequence (Explicit formula)

1. Jul 21, 2015

AKJ1

1. The problem statement, all variables and given/known data
{ 7/6 , 45/54 , 275/648, 1625/9720 ... }

Problem from a practice exam. My instructions are to find an explicit formula for the above sequence..

3. The attempt at a solution

Let An =7/6 , 45/54 , 275/648, 1625/9720 ...

Allow An = Bn / Cn

Bn = 7, 45, 275, 1625.... (2n+5) 5n-1 starting at n = 1

Cn = 6,54,648,9720.... 3(n+1) [ What multiplies here is the preceding term, so if we allow n = 2 , we multiply the expression by 6 to get 54, if we allow n = 3, we multiply by 54 to get 648, if we allow n = 4, we multiply by 648 to get 9720.

I have no idea how to express this, or if there is a better way.

Last edited: Jul 21, 2015
2. Jul 21, 2015

cpsinkule

Cn=Cn-13(n+1) and declare that C0=1

3. Jul 21, 2015

AKJ1

∴ Starting at n=1 An = (2n+5) 5n-1 / 3(n+1) Cn-1 , where we have declared C0 = 1

Noting that Bn & Cn equal what we have defined above.

Correct?

4. Jul 21, 2015

cpsinkule

The entire sequence can't be indexed by two letters, A and C, you need to find a form where you only need A

5. Jul 21, 2015

AKJ1

So I have to rewrite Cn in terms of A only? Is this possible? I am drawing a complete blank

6. Jul 22, 2015

AKJ1

Figured it out!