i)an+1-2an=5, n>=0, a0=1
ii)an+1=an+(2n+3), n>=0, a0=1
For the second one, write: (this is a telescopic sum), from which you deduce, using your equation, (remember ).
For the first one, you know , so the telescopic trick doesn't work directly. However, it works for : we have . A telescopic summation gives: (remember the sum of terms in a geometric sequence)