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

question 294

Multiple Choice

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) \(\frac { 5 + 2 \sqrt { 2 } } { 3 }\)

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