We have to recurrence relation an = 2an-1 - an-2. Find a2 and a3 if

Question

We have to recurrence relation an = 2a_n-1 - a_n-2. Find a₂ and a₃ if:

 

a) a₀ = 1 og a₁ = 0?

 

b) a₀ = 0 og a₁ = 1?

 

c) a₀ = 1 og a₁ = 2?

Answer 1

So, we have a relationship: an = 2 a_n-1 - a_n-2 . Plugging in n = 2, and then n = 3: 

 

n = 2: a2 = 2*a1 - a0

n = 3: a3 = 2*a2 - a1

 

For a) a0 = 1, a1 = 0: 

 

n = 2: a2 = 2*0 - 1 = -1

n = 3: a3 = 2* (-1) - 0 = -2

 

Try and solve the next two using this same procedure, but replace the values for a0 and a1.