blog assignment

1. I have problems with recursive definitions. Sometimes I come up with a formula that works for such sequence but then I check the answer in the back of the book and there is a different formula that works as well for the sequence. Also, the geometric and arithmetic formulas to find the nth, term also work, however I don't understand the difference on whether or not these are recursive or explicit definitions.

2. T1= 4, T(2)=8 T(4)= 16
Find the 30th term

tn=t1+(n-1)d

t(30)=4+(29)4