Answer: 125
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Work Shown:
f(1) = 3.2 is the first term
Use this to find f(2). Plug in x = 1
f(x+1) = (5/2)*f(x)
f(1+1) = (5/2)*f(1)
f(2) = (5/2)*3.2
f(2) = 2.5*3.2
f(2) = 8
Then use this to find f(3). Plug in x = 2
f(x+1) = (5/2)*f(x)
f(2+1) = (5/2)*f(2)
f(3) = (5/2)*f(2)
f(3) = (5/2)*8
f(3) = 2.5*8
f(3) = 20
Use this to find f(4). Plug in x = 3
f(x+1) = (5/2)*f(x)
f(3+1) = (5/2)*f(3)
f(4) = (5/2)*f(3)
f(4) = (5/2)*20
f(4) = 2.5*20
f(4) = 50
Use this to find f(5). Plug in x = 4
f(x+1) = (5/2)*f(x)
f(4+1) = (5/2)*f(4)
f(5) = (5/2)*f(4)
f(5) = (5/2)*50
f(5) = 2.5*50
f(5) = 125