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? $f(n + 1)=f(n + 1)+110$ $f(n + 1)=f(n + 1)+20$ $f(n + 1)=f(n)+20$

Explanation:

Step1: Analyze the sequence

The given sequence is \(110,130,150,170,\cdots\). The common difference \(d\) between consecutive terms is \(130 - 110=20\), \(150 - 130 = 20\), \(170-150=20\).

Step2: Recall the recursive formula for an arithmetic sequence

The recursive formula for an arithmetic sequence is \(f(n + 1)=f(n)+d\), where \(d\) is the common difference. Here \(d = 20\).

Answer:

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