The sequence is #{3,15,75,375}#
So #f(1)=3#, which is true for all of the sequences, so that only kind of helps.
For (1) we know #f(n) = 5*f(n-1)# so #f(2) = 5*f(1) = 5(3) =15#, so that's still an option. #f(3)=5*f(2) = 5*15=75#, #f(4)=5*f(3) = 5*75 = 375# all work.
For (2) we know #f(n) = 1/5*f(n-1)# so #f(2) = 1/5*f(1) = 1/5(3) =3/5#, so that's out.
For (3) we know #f(n) = 12+f(n-1)# so #f(2) = 12+f(1) = 12+3 =15#, so that's still an option. Let's find #f(3) = 12+f(2)=12+15=27 ne 75# so this option is out.
For (4) we know #f(n) = -12+f(n-1)# so #f(2) = -12+f(1) =-12+3=-9#, so this option is out.
The only one that works is (1)
