Find the Value of the Limit of the Sequence Defined $$a _ { 1 } = 1 , a _ { n + 1 } = 6 - \frac { 1 } { a _ { n } }$$

Multiple Choice

Find the value of the limit of the sequence defined by
$$a _ { 1 } = 1 , a _ { n + 1 } = 6 - \frac { 1 } { a _ { n } }$$
Select the correct answer.

A) $\frac { 6 + \sqrt { 5 } } { 2 }$
B) $\frac { 6 - \sqrt { 10 } } { 2 }$
C) $\frac { 6 + \sqrt { 10 } } { 2 }$
D) $\frac { 6 - \sqrt { 5 } } { 2 }$
E) $6 + \sqrt { 10 }$