Solving Homogenous Linear Recurrence Relations Using Method of Characteristic Roots (Another Method To Solve Recurrence Equations)

The term linear means that each term of the sequence is defined as a linear function of the preceding terms. The coefficients and the constants may depend on n, even non-linearly. Homogeneous means that the constant term of the relation is zero.

Substituting this in original recurrence relation, we have

or, (r – 2) (r – 3) = 0

=> r₁ = 2 r₂ = 3

=> a_n = 2ⁿ or, a_n = 3ⁿ; both work