Question

Is there a strategy to approaching a problem like this?

Answer 1

It is a geometric mean sequence.
the 2nd term is 20, the 5th term is 0.16
so the next 3 terms are found by multiplying successive terms by the constant x.  20x^3 = 0.16 which is derived by multiplying 20 by x, three times to get 0.16
So x^3 =.008
x=0.2
The first term is found by saying a1^.2 = 20, so a1 = 100
When n =  1     2   3   4    5
     t(n) = 100 , 20, 4, .8, .16