Question

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

Answer 1

A sequence is defined by the recursive function then f(1) is 81

Solution:

Given that,

A sequence is defined by the recursive function:

$f(n+1) = \frac{1}{3} \times f(n)$ ------ eqn 1

Given that,

$f(3) = 9$

Substitute n = 2 in eqn 1

$f(2 + 1) = \frac{1}{3} \times f(2)\\\\f(3) = \frac{1}{3} \times f(2)\\\\Substitute\ f(3) = 9\\\\9 = \frac{1}{3} \times f(2)\\\\f(2) = 27$

Substitute n = 1 in eqn 1

$f(1 + 1) = \frac{1}{3} \times f(1)\\\\f(2) = \frac{1}{3} \times f(1)\\\\Substitute\ f(2) = 27\\\\27 = \frac{1}{3} \times f(1)\\\\f(1) = 27 \times 3\\\\f(1) = 81$

Thus f(1) is 81