Answer:
f(1) = 81
Explanation:
given is f(n + 1) = 1/3f(n)
f(3) = 9
ayou need to find f(0) before you can answer what is f(1).
Just start by applying for...
n=0
f(0+1) = 1/3 * f(0)
f(1) = 1/3 * f(0)
n=1
f(1+1) = 1/3 * 1/3*f(0)
f(2) = 1/9 * f(0)
n=2
f(2+1) = 1/3 * 1/9* f(0)
f(3) = 1/27 * f(0)
But it is given that f(3) = 9 so substitute this in the line above to calculate the value of f(0)....
9 = 1/27 * f(0)
Multiply left and right of the = sing by 27 gives
f(0) = 27 * 9
f(0) = 243
We already know this next line because we started with n=0
f(1) = 1/3 * f(0)
Substitute f(0) = 243 in the line above to finally calculate the value of f(1).
f(1) = 1/3 * 243
f(1) = 81