Use Inductive Reasoning to Predict the Next Equation A) B)

question 27

Multiple Choice

Use inductive reasoning to predict the next equation.
- $\begin{array} { r } \frac { 1 } { 3 } = \frac { 1 } { 2 } \left( 1 - \frac { 1 } { 3 } \right) \\\frac { 1 } { 3 } + \frac { 1 } { 9 } = \frac { 1 } { 2 } \left( 1 - \frac { 1 } { 9 } \right) \\\frac { 1 } { 3 } + \frac { 1 } { 9 } + \frac { 1 } { 27 } = \frac { 1 } { 2 } \left( 1 - \frac { 1 } { 27 } \right) \\\frac { 1 } { 3 } + \frac { 1 } { 9 } + \frac { 1 } { 27 } + \frac { 1 } { 81 } = \frac { 1 } { 2 } \left( 1 - \frac { 1 } { 81 } \right) \end{array}$

• A) \(\frac { 1 } { 3 } + \frac { 1 } { 9 } + \frac { 1 } { 27 } + \frac { 1 } { 81 } + \frac { 1 } { 243 } = \frac { 1 } { 2 } \left( 1 - \frac { 1 } { 243 } \right)\)
• B) \(\frac { 1 } { 3 } + \frac { 1 } { 9 } + \frac { 1 } { 27 } + \frac { 1 } { 81 } + \frac { 1 } { 729 } = \frac { 1 } { 2 } \left( 1 - \frac { 1 } { 729 } \right)\)
• C) \(\frac { 1 } { 3 } + \frac { 1 } { 9 } + \frac { 1 } { 27 } + \frac { 1 } { 81 } + \frac { 1 } { 162 } = \frac { 1 } { 2 } \left( 1 - \frac { 1 } { 162 } \right)\)
• D) \(\frac { 1 } { 3 } + \frac { 1 } { 9 } + \frac { 1 } { 27 } + \frac { 1 } { 81 } + \frac { 1 } { 243 } = \frac { 1 } { 3 } \left( 1 - \frac { 1 } { 243 } \right)\)

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Definitions:

Passed By Legislature

A bill or proposed law that has been approved by both houses of a legislative body and is awaiting further action, such as executive approval, to become law.

Nash Equilibrium

Nash Equilibrium is a concept in game theory where each participant's strategy is optimal considering the strategies of other participants, implying no player has anything to gain by changing only their own strategy.

Prisoners' Dilemma

A scenario in game theory where two individuals acting in their own self-interest do not achieve the optimal outcome.

Payoffs

The outcomes or rewards received as a result of choosing a particular strategy or course of action.