A Sequence $c _ { 0 } , c _ { 1 } , c _ { 2 } , \ldots$

question 10

Essay

A sequence $c _ { 0 } , c _ { 1 } , c _ { 2 } , \ldots$ satisfies the recurrence relation $c _ { k } = 6 c _ { k - 1 } - 9 c _ { k - 2 }$ with initial conditions $c _ { 0 } = 1$ and $c _ { 1 } = 6$ . Find an explicit formula for the sequence.

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Definitions:

Demand Curve

A graphical representation of the relationship between the price of a good or service and the quantity demanded for a given period.

Normal Goods

Goods for which demand increases when income increases, and falls when income decreases, but price remains constant.

Inferior Goods

Products whose demand decreases as the income of consumers increases, reflecting a preference shift to higher-quality substitutes when affordability allows.

Price Elasticity

An assessment of the responsiveness of the demand for a product to variations in its price.