Question 72
The sequence $\{x_{n}\}_{n=1}^{\infty}$ is defined by $x_{1}=2$ and $x_{n+1}=1+a x_{n}$, $n \geq 1$, where $a$ is a real number. Find all values of $a$ for which the sequence is:
a) an arithmetic progression;
b) convergent and find its limit.
a) an arithmetic progression;
b) convergent and find its limit.