tmua.me Extreme Set A Paper 2 · Question 19

A sequence of real numbers is defined by

0<x_1<1,\qquad x_{n+1}=|2x_n-1|\quad(n\geq1).

Consider the condition that $x_n=x_1$ for some integer $n>1$ , and the statement that $x_1$ is rational.

Which of the following correctly describes the condition in relation to the statement?

AThe condition is necessary but not sufficient.

BThe condition is sufficient but not necessary.

CThe condition is both necessary and sufficient.

DThe condition is neither necessary nor sufficient.

examday