Question

The Fibonacci sequence is defined by 1 = a₁ = a₂ and a_n = a_{n – 1} + a_{n – 2} , n > 2.

Find a_n+1/a_n, for n = 1, 2, 3, 4, 5

Answer 1

Using the formula for the Fibonacci sequence, you get the following results: 

a(1) = 1 
a(2) = 1 
a(3) = 2 
a(4) = 3 
a(5) = 5 
a(6) = 8 

These are the terms we need to use to solve the problem. In general, the a(n) term is defined as the sum of the previous two terms. 

Now we can solve a(n+1)/a(n) for each case: 

n = 1 -> a(2)/a(1) = 1/1 = 1 
n = 2 -> a(3)/a(2) = 2/1 = 2 
n = 3 -> a(4)/a(3) = 3/2 = 1.5 
n = 4 -> a(5)/a(4) = 5/3 = 1.667 
n = 5 -> a(6)/a(5) = 8/5 = 1.6