is it correct way to solve this? if not then please provide me the solution
No, it is wrong. It is non homogeneous recurrence relation.
I have done the simplification,now you just need to put the value of a_{0 }a_{1} and get the answer
as the rhs of equation 2.1^{n} so we tool a trial of 2A1^{n}
and put this value to original equation
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