For large nnn, which term dominates in the solution an=2⋅5n+3⋅2na_n = 2 \cdot 5^n + 3 \cdot 2^nan=2⋅5n+3⋅2n?
The 2⋅5n2 \cdot 5^n2⋅5n term dominates
The 3⋅2n3 \cdot 2^n3⋅2n term dominates
Both terms grow equally fast
The sequence converges to 0