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) $a _ { n } = 3 ^ { n } + 6 ^ { n }$