Verify That $a _ { n } = 3^{n}$ Is a Solution to the Recurrence Relation

question 170

Short Answer

Verify that $a _ { n } = 3^{n}$ is a solution to the recurrence relation $a _ { n } = 4 a _ { n - 1 } - 3 a _ { n - 2 }$

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Definitions:

Shared Ancestry

Shared ancestry refers to the genetic heritage that individuals have in common with their biological family or ethnic group, tracing lineage through genetics and cultural heritage.

Cultural Heritage

The legacy of physical artifacts and intangible attributes of a group or society, including traditions, languages, and values passed down through generations.

Symbolic Ethnicity

A form of ethnicity where attachment to one’s cultural heritage is voluntary, individualistic, and often void of the obligations felt by members of the same ethnic group in past generations.

Casimir Pulaski Day

An observed day in some U.S. states honoring Casimir Pulaski, a Revolutionary War cavalry officer born in Poland, celebrated for his contributions to U.S. independence.