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

question 117

Multiple Choice

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

• 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) \(6 + \sqrt { 10 }\)

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Definitions:

Mutually Exclusive

Events that cannot happen simultaneously.

Simple Events

In probability, a simple event is a single outcome within a sample space, not composed of other events.

Probability

A measure of the likelihood that an event will occur, ranging from 0 (impossibility) to 1 (certainty).

Combinations

The selection of items from a collection such that the order of selection does not matter.