Geometric Sequence and Recursive Definition

[rought]

Homework Statement

In a Geometric Sequence find t₁₀. t₃ = 4 and t₆= 4/27

Give a recursive definition for the sequence: 1, 4, 13, 40...

Homework Equations

I know that a Geometric sequence is: t_n=t₁(r)^n-1

And that a recursive formula starts off with t_n-1

I'm not sure where to go from here...

 

[Mark44]

A geometric sequence has terms that look like this: {a, ar, ar², ar³, ...}, where each term is r time the previous term. In your first problem, you have t₃ = 4, so t₄ = rt₃ = 4r, t₅ = 4t₄ = ? Just work your way up to the ones you want to find.

In your second problem, you have {1, 4, 13, 40, ...}
The 2nd term is the first plus 3. The 3rd term is 9 plus the 2nd. The 4th term is 27 + the 3rd. Do you see a pattern?