how could this one $\displaystyle (-3)(2)^{n-1} + 2^n(-1)$ simplify to $\displaystyle -2^{n+2}+3$?
Yeh! that's right!
I was just keep checking it "$\displaystyle -2^{n+2}+3$" against "$\displaystyle a_n = 2a_{n-1} -3 , a_0=-1$" for n terms and it was true.
So "$\displaystyle (-3)(2)^{n-1} + 2^n(-1)$" is not right! I suppose it must be something wrong in somewhere.
Thank you!