The value of f(1) for the recursive function is (d) 81
The recursive function is given as:
[tex]f(n + 1) = \frac 13f(n)[/tex]
Multiply both sides of the equation by 3
[tex]3f(n + 1) = f(n)[/tex]
Rewrite as:
[tex]f(n) = 3f(n + 1)[/tex]
Set n = 2;
[tex]f(2) = 3f(2 + 1)[/tex]
[tex]f(2) = 3f(3)[/tex]
Set n = 1 in [tex]f(n) = 3f(n + 1)[/tex]
[tex]f(1) = 3f(1 + 1)[/tex]
[tex]f(1) = 3f(2)[/tex]
Substitute [tex]f(2) = 3f(3)[/tex]
[tex]f(1) = 3 \times 3f(3)[/tex]
[tex]f(1) = 9f(3)[/tex]
Substitute 9 for f(3)
[tex]f(1) = 9 \times 9[/tex]
[tex]f(1) = 81[/tex]
Hence, the value of f(1) for the recursive function is (d) 81
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