Question

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

Answer 1

Answer:

      f(1) = 81

Step-by-step explanation:

Multiplying the given relation

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

by 3 gives

f(n) = 3 f(n + 1).      ...(*)

Putting n=2 into (*) gives

f(2) = 3 f(2 + 1) = 3 f(3) = 3×9 = 27

Putting n=1 into (*) gives

f(1) = 3 f(1 + 1) = 3 f(2) = 3×27 = 81