Verify That $a _ { n } = 7 \cdot 3 ^ { n } - \pi$

question 97

Essay

Verify that $a _ { n } = 7 \cdot 3 ^ { n } - \pi$ is a solution to the recurrence relation $a _ { n } = 4 a _ { n - 1 } - 3 a _ { n - 2 }$

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Definitions:

Labor Earnings

Income received by workers for their labor services, including wages, salaries, and other forms of compensation.

Government Policy

Actions or inactions chosen by government officials to address specific public issues, ranging from economic regulations to social welfare programs.

Natural Rate

Often refers to the natural rate of unemployment, which is the level of unemployment consistent with a stable rate of inflation, or the equilibrium rate unaffected by short-term fluctuations.

Fully Employed

Refers to a situation where all available labor resources are being used in the most economically efficient way.