Provide an Appropriate Response $\left\{ r _ { n } \right\}$

Multiple Choice

Provide an appropriate response.
-A sequence of rational numbers $\left\{ r _ { n } \right\}$ is defined by $r _ { 1 } = \frac { 1 } { 1 }$ , and if $r _ { n } = \frac { a } { b }$ then $r _ { n } + 1 = \frac { a + 5 b } { a + b }$ . Find $\lim _ { n \rightarrow } r _ { n }$ . Hint: Compute the square of several terms of the sequence on a calculator.

A) 2
B) $\sqrt { 6 }$
C) $\sqrt { 10 }$
D) $\sqrt { 5 }$