Consider the bisection method starting with the interval $[1.5, 3.5]$
(a) What is the width of the interval at the nth step of this method?
(b) What is the maximum distance possible between the root and the midpoint of this interval?
For (a), I know that $b_n-a_n=2^{-n}(b_0-a_0)$ with which $b_n-a_n=2^{-n}(b_0-a_0)=2^{-n}(3.5-1.5)=2^{-n+1}$, but in the answers of the book says that it must be $2^{-n+2}$, could someone explain to me why?
For (b), I know that $|r-c_n|\leq2^{-(n+1)}(b_0-a_0)$ and so $|r-c_n|\leq2^{-(n+1)}(b_0-a_0)=2^{-(n+1)}(3.5-1.5)=2^{-n}$, but in the answers to the book says that it must be $2^{-n+1}$, could someone explain why? Thank you very much.
Your book is off by $1$. If you just plug in $n=0$ or $n=1$ you can see your answers are correct.