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

question 10

Short Answer

A sequenceis $\left\{ a _ { n } \right\}$ defined recursively by the equation $a _ { n } = 0.5 \left( a _ { n - 1 } + a _ { n - 2 } \right)$ for $n \geq 3$ where $a _ { 1 } = 14 , a _ { 2 } = 14$ .
Use your calculator to guess the limit of the sequence.

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Definitions:

Economic Trends

Patterns or movements in economic indicators such as GDP, unemployment rates, or consumer confidence that indicate the general direction of an economy.

Taxation Depreciation

The allowance for the depreciation of assets that can be deducted from taxable income for tax purposes.

Accounting Depreciation

Accounting depreciation is the systematic allocation of the cost of a tangible asset over its useful life, reflecting its consumption, wear and tear, or obsolescence.

After-Tax Consequences

The financial results of an event or transaction taking into account the effects of taxes.