A Geometric Sequence Is Given $$\left\{ 2 \left( \frac { 1 } { 2 } \right) ^ { n - 1 } \right\}$$

question 64

Multiple Choice

A geometric sequence is given. Find the common ratio and write out the first four terms.
- $$\left\{ 2 \left( \frac { 1 } { 2 } \right) ^ { n - 1 } \right\}$$

• A) \(a _ { n } = 2 \cdot ( 2 ) ^ { n - 1 }\)
• \(\mathrm { r } = 2 ; 2,4,8,16 , \ldots\)
• B) \(a _ { n } = 2 \left( \frac { 1 } { 4 } \right) ^ { n - 1 }\)
• \(\mathrm { r } = \frac { 1 } { 4 } ; 2 , \frac { 1 } { 2 } , \frac { 1 } { 8 } , \frac { 1 } { 32 } , \ldots\)
• C) \(a _ { n } = 2 \left( \frac { 1 } { 2 } \right) ^ { n - 1 }\)
• \(\mathrm { r } = \frac { 1 } { 2 } ; 2,1 , \frac { 1 } { 2 } , \frac { 1 } { 4 } , \ldots\)
• D) \(\mathrm { a } _ { \mathrm { n } } = \frac { 1 } { 2 } ( 2 ) ^ { \mathrm { n } - 1 }\)
• \(\mathrm { r } = \frac { 1 } { 2 } ; 2,4,8,16 , \ldots\)

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The inherent features of an investment that determine its potential return and the likelihood of loss.

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The theoretical rate of return on an investment with zero risk, typically associated with government bonds.

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The extra return that investors require to hold a risky market portfolio instead of risk-free assets.

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