First one :
an = (2/5)(5)n - 1
Recursive rule : a1 = 2/5 an = 5an-1
Second one :
a1 = 2 an = (1/3)an-1
Explicit Rule : an = 2(1/3)n-1
Third one
6, -18, 54, -162 [ note that the common ratio = -3 ]
Recursive Rule : a1 = 6 an = (-3)an-1
Fourth one : 9, 6, 4, 8/3
The common ratio is : 6 / 9 = 2/3
Explicit Rule : an = 6(2/3)n-1