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? options: f(n + 1) = f(n) + 20; f(n + 1) = f(n) + 110; f(n + 1) = f(n + 1) + 20; f(n + 1) = f(n + 1) + 110

Explanation:

Step1: Analyze the sequence

The sequence is \( 110,130,150,170,\cdots \).

Step2: Calculate the common difference

\( 130 - 110=20 \), \( 150 - 130 = 20 \), \( 170-150=20 \).

Step3: Determine the recursive formula

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

Answer:

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