Solution to Recurrence Relation: an = 2an−1 + an−2 − 2an−3

Math Problem Statement

To find the solution to the recurrence relation

−

an =2an−1 +an−2 −2an−3

with initial conditions

a0 =3,

a1 =6, and

a2 =0, you need to follow these steps:

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Algebra
Recurrence Relations
Characteristic Equations
Polynomial Factorization

Recurrence relation: an = 2an−1 + an−2 − 2an−3
Characteristic equation: r^3 - 2r^2 - r + 2 = 0

Rational Root Theorem
General Solution of Recurrence Relations

Grades 10-12

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