Let

question 46

Essay

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

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Definitions:

Lincoln's Reelection

Refers to the 1864 presidential election in the United States, where Abraham Lincoln won a second term in office as President during the Civil War.

September 1864

A specific timeframe during the American Civil War, marked by several military engagements and strategic developments.

Appomattox Court House

The site of the surrender of Confederate General Robert E. Lee to Union General Ulysses S. Grant, effectively ending the American Civil War on April 9, 1865.

Ten-Percent Plan

A reconstruction plan proposed by Abraham Lincoln that allowed a rebel state to rejoin the Union once 10% of its voters pledged allegiance to the U.S. and abolished slavery.