@aditi19
your answer is correct.
You can verify yourself by taking small values of 'n'.
For eg., for $n=1$, recurrence relation gives $a_1=3a_0+2^1=3*1+2=5$
Now,$-2^{n+1}$ will give answer as $-2^2=-4$ where as $3^{n+1}-2^{n+1}$ will give answer as $3^2-2^2=5$. So, your answer is correct.