The Sequence Is Defined Recursively $a _ { 1 } = \sqrt { 6 } ; a _ { n } = \sqrt { 6 a _ { n - 1 } }$

question 43

Multiple Choice

The sequence is defined recursively. Write the first four terms.
- $a _ { 1 } = \sqrt { 6 } ; a _ { n } = \sqrt { 6 a _ { n - 1 } }$

• A) \(\sqrt { 6 } , \sqrt { 6 \sqrt { 6 } } , \sqrt { 6 \sqrt { 6 \sqrt { 6 } } } , \sqrt { 6 \sqrt { 6 \sqrt { 6 \sqrt { 6 } } } }\)
• B) \(\sqrt { 6 } , 6 \sqrt { 6 } , 36 \sqrt { 6 } , 216 \sqrt { 6 }\)
• C) \(\sqrt { 6 } , 6,6 \sqrt { 6 } , 36\)
• D) \(\sqrt { 6 } , \sqrt { \sqrt { 6 } } , \sqrt { \sqrt { \sqrt { 6 } } } , \sqrt { \sqrt { \sqrt { \sqrt { 6 } } } }\)

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Definitions:

Production Possibilities Frontier

A curve depicting all maximum output possibilities for two goods, given a set of inputs.

Utility

In economics, it represents a measure of satisfaction or happiness that consumers derive from the consumption of goods and services.

Efficient

The optimal allocation of resources to maximize the production of goods and services without wasting those resources.

Production Possibilities Frontier

A curve that shows the maximum efficient production level of one good for a given level of production for another, assuming fixed resources and technology.