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? a. f(n) = 5n − 1 b. f(n) = 5n + 1 c. f(n) = 4n + 1 d. f(n) = 4n − 1

Answer:The rule is [tex]\implies f(n)=4n+1[/tex]Step-by-step 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:[tex]5,9,13,17[/tex]The y-values form a sequence. The first term of this sequence is: [tex]a=5[/tex]The common difference of this sequence is [tex]d=9-4=5[/tex]The rule is given by:[tex]f(n)=a+d(n-1)[/tex]We substitute the values to obtain:[tex]f(n)=5+4(n-1)[/tex][tex]\implies f(n)=5+4n-4[/tex]The rule is [tex]\implies f(n)=4n+1[/tex]