Middle School

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------------------------------------------------ A sequence is defined by the recursive function [tex]f(n + 1) = \frac{1}{3} f(n)[/tex]. If [tex]f(3) = 9[/tex], what is [tex]f(1)[/tex]?

A. 1
B. 3
C. 27
D. 81

Answer :

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

Solution:

Given that,

A sequence is defined by the recursive function:

[tex]f(n+1) = \frac{1}{3} \times f(n)[/tex] ------ eqn 1

Given that,

[tex]f(3) = 9[/tex]

Substitute n = 2 in eqn 1

[tex]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[/tex]

Substitute n = 1 in eqn 1

[tex]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[/tex]

Thus f(1) is 81

Answer:

D 81

Step-by-step explanation: