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

question 148

Short Answer

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:

Heat Transfer

The movement of heat from a warmer object to a cooler one, which can occur through conduction, convection, or radiation.

Convection

Transfer of thermal energy by flow of a liquid or a solid, but weak material.

Heating During Burial

An increase in temperature experienced by rocks and sediments as they are buried deeper in the Earth’s crust, leading to changes in their properties and structure.

Liquid-Solid Boundary

The interface where a liquid phase and a solid phase meet, significant in studies of material properties and phase transitions.