Consider the Recurrence Relation $a _ { n } = 3 a _ { n - 1 } + 5 ^ { n }$

question 31

Short Answer

Consider the recurrence relation $a _ { n } = 3 a _ { n - 1 } + 5 ^ { n }$ (a) Write the associated homogeneous recurrence relation. (b) Find the general solution to the associated homogeneous recurrence relation. (c) Find a particular solution to the given recurrence relation. (d) Write the general solution to the given recurrence relation. (e) Find the particular solution to the given recurrence relation when a0 = 1.

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Definitions:

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