The Solutions To $a _ { n } = - 3 a _ { n - 1 } + 18 a _ { n - 2 }$

question 59

Short Answer

The solutions to $a _ { n } = - 3 a _ { n - 1 } + 18 a _ { n - 2 }$ have the form $a _ { n } = c \cdot 3 ^ { n } + d \cdot ( - 6 ) ^ { n }$ Which of the following are solutions to the given recurrence relation?
(a) $a _ { n } = 3 ^ { n + 1 } + ( - 6 ) ^ { n }$
(b) $a _ { n } = 5 ( - 6 ) ^ { n }$
(c) $a _ { n } = 3 c - 6 d$
(d) $a _ { n } = 3 ^ { n - 2 }$
(e) $a _ { n } = \pi \left( 3 ^ { n } + ( - 6 ) ^ { n } \right)$
(f) $a _ { n } = - 3 ^ { n }$
(g) $a _ { n } = 3 ^ { n } \left( 1 + ( - 2 ) ^ { n } \right)$
(h) $a _ { n } = 3 ^ { n } + 6 ^ { n }$

---

Definitions:

Fictitious Business Names

Aliases under which individuals or businesses operate that are different from their legal, registered names, often registered with local or state governments.

Professionals

Individuals who possess specialized knowledge or skills in a particular field, often requiring certification or licensing.

Management Flexibility

The ability of a business's management team to adapt to changes or challenges in the operating environment, including strategic decision-making.

Personal Liability

The legal responsibility of an individual to compensate for harm or damages their actions have caused, potentially affecting their personal assets.