July 2010
Intermediate to advanced
576 pages
13h 3m
English
Content preview from Discrete Mathematics
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3
Recurrence Relations
A recurrence relation relates the nth term of a sequence to its predecessors. These relations are related to recursive algorithms.
3.1 RECURRENCE RELATIONS
Definition 3.1
A recurrence relation for a sequence a0, a1, a2, … is a formula (equation) that relates each term an to certain of its predecessors a0, a1, …, an − 1.
The initial conditions for such a recurrence relation specify the values of a0, a1, a2, …, an − 1.
For example, recursive formula for the sequence
3, 8, 13, 18, 23
is
a1 = 3, an = an − 1 + 5, 2 ≤ n < ∞.
Here, a1 = 3 is the initial condition.
Similarly, the infinite sequence
3, 7, 11, 15, 19, 23, …
can be defined by the recursive formula
a1 = 3, an = an − 1 + 4, 2 ≤ n < ∞.
EXAMPLE 3.1
Find the sequence ...
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