If $a _ { 1 } = 1$ And $a _ { n + 1 } = 3 - \left( \frac { 1 } { a _ { n } } \right)$

If $a _ { 1 } = 1$ and $a _ { n + 1 } = 3 - \left( \frac { 1 } { a _ { n } } \right)$ for $n \geq 1$ , find the limit of the sequence $a _ { n }$ .

A) 2
B) $\sqrt { 2 }$
C) $\sqrt { 3 }$
D) $\sqrt { 5 }$
E) $\frac { 2 + \sqrt { 3 } } { 4 }$
F) $\frac { 3 + \sqrt { 5 } } { 2 }$
G) $\frac { 5 + \sqrt { 7 } } { 2 }$
H) $\frac { 5 + 2 \sqrt { 2 } } { 3 }$

Correct Answer:

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