Sequences Question

[kalyan601]

Hi, I need help with this question. If u1 is 1, how would I then find u₂, u₃, u₄ and eventually u₂₀?

The sequence of positive numbers u₁ u₂, u₃, ... is given by u_n + 1 = (u_n – 3)², u₁ = 1.
(a) Find u₂, u₃ and u₄.
(b) Write down the value of u₂₀.

Thanks for your help!

 

[Ishuda]

I believe you made a typo and the equation should read
u_{n + 1} = (u_n – 3)², u₁ = 1.

If that is the case we would have
u₂ = (u₁ – 3)²
u₃ = (u₂ – 3)²
u₄ = (u₃ – 3)²
etc.

So
u₂ = (1 - 3)² = (-2)² = 4

If, after computing several values you see a pattern, you could possibly deduce what all values would be in a simpler forumla.