Question

A sequence is defined by the recursive formula f (n + 1) = f(n) – 2. If f(1) = 18, what is f(5)?

Answer 1

Answer: The answer is 10.

Step-by-step explanation: The recursive formula of the sequence is given by

`f(n+1)=f(n)-2.`

We are to find the value of f(5) if f(1) is 18.

We have

`f(2)=f(1)-2=18-2=16,\\\\f(3)=f(2)-2=16-2=14,\\\\f(4)=f(3)-2=14-2=12,\\\\f(5)=f(4)-2=12-2=10.`

Thus, the value of f(5) is 10.

Answer 2

Lets solve f(5). First, replace all "n"s in the equation with 5s. F(5+1)=F(5)-2. This means that F(6)=F(5)-2, F(5)=F(4)-2, F(4)=F(3)-2, F(3)=F(2)-2, and F(2)=F(1)-2. Because we know F(1)=18, F(2)=16, F(3)=14, F(4)=12, and F(5)=10.

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