[Solved] \[\text { Let } a _ { 1 } = 2 , a _ { 2 } = 9 \text {, and } a _ { n } = 2 a _ { n - 1 } + 3 a _ { n - 2 } \text { for } n \geq 3 \text {. Show that } a _ { n } \leq 3 ^ { n } \text { for all positive integers } n \text {. }\] Electroencephalographs (EEGs): Devices that measure the electrical activity of the brain through electrodes placed on the scalp. Electroencephalograph (EEG): A device used to record the electrical activity of the brain, often used in the diagnosis of neurological conditions. Epileptic Seizure: A burst of uncontrolled electrical activity between brain cells (neurons) that causes temporary abnormalities in muscle tone or movements (stiffness, twitching, or limpness), behaviors, sensations, or states of awareness. Electrical Activity: The movements or flow of electrical charges (ions) within or between cells, tissues, or organs, which are fundamental for various physiological processes including nerve impulse transmission and muscle contraction.

Solved

question 10

Essay

$\text { Let } a _ { 1 } = 2 , a _ { 2 } = 9 \text {, and } a _ { n } = 2 a _ { n - 1 } + 3 a _ { n - 2 } \text { for } n \geq 3 \text {. Show that } a _ { n } \leq 3 ^ { n } \text { for all positive integers } n \text {. }$

Definitions:

Electroencephalographs (EEGs)

Devices that measure the electrical activity of the brain through electrodes placed on the scalp.

Electroencephalograph (EEG)

A device used to record the electrical activity of the brain, often used in the diagnosis of neurological conditions.

Epileptic Seizure

A burst of uncontrolled electrical activity between brain cells (neurons) that causes temporary abnormalities in muscle tone or movements (stiffness, twitching, or limpness), behaviors, sensations, or states of awareness.

Electrical Activity

The movements or flow of electrical charges (ions) within or between cells, tissues, or organs, which are fundamental for various physiological processes including nerve impulse transmission and muscle contraction.