two consecutive terms in geometric sequences

Question

How do I solve

If f(3)=5 and f(4)=10

f(5)=____ and f(6)=____. Recursive function: _______________

Answer 1

Since this is a geometric sequence, the general formula is f(n) = f(1)*r^(n-1)

Given : f(3)=5 and f(4) = 10

or

5 = f(1)* r^2

10 = f(1)*r^3

Solving for f(1) and r we find: f(1) = 5/4 and r = 2

So f(5) = 20, f(6) = 40 and the recursion function is f(n) = 5/4*2^(n-1)