The characteristic equation is

 r − 3 = 0

The solution is r = 3. The general solution has the form

 a_n = c₁3ⁿ

Since a₀ = 2, we have

 2 = a₀ = c₁3⁰

So c₁ = 2, and the solution is

 a_n = 2(3ⁿ)