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

question 19

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:

Law Of Effect

A psychological principle suggesting that behaviors followed by positive outcomes are likely to be repeated, whereas those followed by negative outcomes are less likely to be repeated.

Reinforcement Theory

A concept in behavioral psychology based on the idea that behavior can be shaped by controlling the consequences to those behaviors, emphasizing the use of reinforcement and punishment.

Behavioural Consequences

The outcomes or results that follow an individual's actions or behaviors, which can influence future behavior.

Profit-sharing

A company policy of distributing a portion of its profits to its employees as a form of bonus or incentive.