Question

Larry is using an online calculator to calculate the outputs f(n) for different inputs n. The ordered pairs below show Larry's inputs and the corresponding outputs displayed by the calculator: (1, 5), (2, 9), (3, 13), (4, 17) Which of the following functions best represents the rule that the calculator uses to display the outputs? f(n) = 5n − 1 f(n) = 5n + 1 f(n) = 4n + 1 f(n) = 4n − 1

Answer 1

(C) f(n) = 4n + 1

Explanation:

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Answer 2

The rule is
`\implies f(n)=4n+1`

Explanation:

The ordered for Larry's inputs and the corresponding outputs displayed by the calculator are:

(1, 5), (2, 9), (3, 13), (4, 17)

We use the y-values of the ordered pairs to obtain the rule.

The y-values are:

`5,9,13,17`

The y-values form a sequence. The first term of this sequence is:

`a=5`

The common difference of this sequence is

`d=9-4=5`

The rule is given by:

`f(n)=a+d(n-1)`

We substitute the values to obtain:

`f(n)=5+4(n-1)`

`\implies f(n)=5+4n-4`

The rule is
`\implies f(n)=4n+1`