Find a General Term an for the Geometric Sequence $$\frac { 1 } { 2 } , \frac { 5 } { 2 } , \frac { 25 } { 2 } , \ldots$$

question 102

Multiple Choice

Find a general term an for the geometric sequence.
- $$\frac { 1 } { 2 } , \frac { 5 } { 2 } , \frac { 25 } { 2 } , \ldots$$

• A) \(\mathrm { a } _ { \mathrm { n } } = \frac { 1 } { 2 } ( 5 ) ^ { \mathrm { n } - 1 }\)
• B) \(a _ { n } = \frac { 1 } { 2 } + 2 ( n - 1 )\)
• C) \(a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 } + 2\)
• D) \(a _ { n } = \frac { 1 } { 2 } + 5 ( n - 1 )\)

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Definitions:

Slope of Budget Line

The rate at which one good can be exchanged for another without changing the overall spending, reflecting trade-offs in consumer choice.

Elasticity of Demand

A measure of how much the quantity demanded of a good responds to a change in the price of that good, with higher elasticity indicating a stronger response.

Change in Price

A variation in the cost of a good or service over a period which can affect demand and supply dynamics in the market.

Price of X

The amount of money required to purchase a specified good or service, indicated here as "X."