Find the first 5 terms of the sequence

Question

If a1=1 and an=(an-1)^2 + 1. 

Answer 1

Hi Hannah,

 

a₁ = 1 and a_n=(a_n-1)^2 + 1

 

a₂ = (a₁-1)^2+1

= (1-1)^2+1

= 1

a3 = (a2-1)^2+1

= (1-1)^2+1

= 1

a4 = (a3-1)^2+1

= (1-1)^2+1

= 1

a5 = (a4-1)^2+1

= (1-1)^2+1

= 1

 

We see that all the terms of this sequence will be the same, i.e., 1.