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A Sequenceis {an}\left\{ a _ { n } \right\} Defined Recursively by the Equation

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A sequenceis {an}\left\{ a _ { n } \right\} defined recursively by the equation an=0.5(an1+an2)a _ { n } = 0.5 \left( a _ { n - 1 } + a _ { n - 2 } \right) for n3n \geq 3 where a1=20,a2=20a _ { 1 } = 20 , a _ { 2 } = 20 . Use your calculator to guess the limit of the sequence.

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Definitions:

Fire Extinguishers

Fire extinguishers are active fire protection devices used to extinguish or control small fires, often in emergency situations.

Subsidized

Financial support provided by the government or other institutions to reduce the cost of services or commodities.

Tax

Compulsory financial charges or levies imposed by a government on individuals or entities to fund public spending and government operations.

Positive Externality

A benefit that affects a party who did not choose to incur that benefit, commonly seen in situations where the activity of one entity leads to positive effects for others.

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