Question

an electrician earns $110 after his first hour of working for a client. his total pay based on the number of hours worked can be represented using the sequence shown. 110, 130, 150, 170,... which recursive formula can be used to determine the total amount of money earned for each successive hour worked based on the amount of money currently earned? f(n + 1)=f(n)+110 f(n + 1)=f(n)+20 f(n + 1)=f(n + 1)+110 f(n + 1)=f(n + 1)+20

Explanation:

Step1: Analyze the sequence difference

Given sequence 110, 130, 150, 170,.... The difference between consecutive terms is \(130 - 110=20\), \(150 - 130 = 20\), \(170-150 = 20\).

Step2: Determine the recursive - formula form

A recursive formula for a sequence is of the form \(f(n + 1)=f(n)+d\), where \(d\) is the common difference between consecutive terms. Here \(d = 20\). So the recursive formula is \(f(n + 1)=f(n)+20\).

Answer:

\(f(n + 1)=f(n)+20\)