Verify that an=2⋅3n−(−1)na_n = 2 \cdot 3^n - (-1)^nan=2⋅3n−(−1)n satisfies the recurrence an=2an−1+3an−2a_n = 2a_{n-1} + 3a_{n-2}an=2an−1+3an−2 by substituting into both sides.
The verification fails; the closed form does not satisfy the recurrence
The formula only works for n≥2n \geq 2n≥2
The verification succeeds; the formula satisfies the recurrence
The formula requires additional initial conditions to confirm