Pablo generates the function fx= 3/2(5/2)^x-1 to determine the xth number in a sequence. which is an equivalent representation?

3/2 = 3 x 1/2 
5/2 = 5 x 1/2 
so f(x) = 3 x 1/2 x (5 x 1/2) ^ x-1
f(x) = 3 x 1 x (5 x 1/2)^x-1   [notice the 1/2 is together]
         
               2

but x/2 = x/1 divided by 2/1 to divide these, invert and multiply: x/2 x 2/1

so f(x) = 3 x 1 x (5/2 )^x-1
             
                         2
     f(x) = 3 (5/2 ) ^ x-1 (x 1/2)

   f(x) = 1.5 (5/2)^x-1

 

61/100, because if it is 0.(value) than it is value / 100 assuming value is 2 digits long. we cannot simplify it further because 61 is prime number.