A sequence is defined by the recursive function f(n + 1) = one-third f(n). If f(3) = 9 , what is f(1) ?

1

Step-by-step explanation:

1/3 x f(3) = f(2 + 1) = 9/3 = 3

1/3 x f(2) = f(1 + 1)  = 3/3 = 1

81

Step-by-step explanation:

The recursive function is given as:

f(n+1)=1/3f(n)

So then we multiply both sides by 3:

3f(n+1)=f(n)

Then we set n=2:

3f(2+1)=f(2)

Which comes to be:

f(2)=3f(3)

Next we set n=1:

f(1)=3f(1+1)

Which is:

f(1)=3f(2)

Then we substitute:

f(1)=3*3f(3)

=9f(3)

=9*9

=81

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