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

question 149

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 $a _ { 1 } = 20 , a _ { 2 } = 20$ . Use your calculator to guess the limit of the sequence.

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Definitions:

Unused Net Operating Losses

Tax deductions that occur when a company's allowable tax deductions are greater than its taxable income within a tax period, which can be carried over to reduce taxable income in future years.

Tax Gains

Refers to the profit that is taxable after selling an asset at a price higher than its purchase price.

Unused Debt Capacity

The additional amount a business or individual can borrow without harming creditworthiness, based on current financial obligations.

Spin-off

A corporate action where a company "spins off" a section as a separate business, leading to the creation of a new independent company.