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eaavendano
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ClosedForm Solution
An equation or formula in which a value can be substituted in order to get a correct output back directly.

Linear
A recurrence relation for a sequence if the earlier values of the sequence appearing in the definition occur only to the 1st power.

Constant Coefficients
Values in an equation which do not change.

FirstOrder
A situation in which the nth term depends only on term n  1.
S(n) = cS(n  1) + g(n)

Homogeneous
A recurrence relation in which the term g(n) = 0 for all n.
S(n) = cS(n  1) + g(n)

Characteristic Equation
The key to the solution of the recurrence relation:
 S(n) c_{1}S(n  1) + c_{2}S(n  2)
 is the quadratic equation:
t^{2}  c_{1}t  c_{2} = 0

