Question

Your father wants you to help him build a shed in the backyard. He says he will pay you $10 for the first week and add an additional $10.50 each week thereafter. The project will take 5 weeks.

How much money will you earn, in total, if you work for the 5 weeks?

I got -0.5 + 10.5n(5) = 52 but apparently its wrong. I don t know how.

Im supposed to be using the arithmetic sequence formula.

Answer 1

So the equation for arithmetic sequences is f(n)= d(n-1)+f(1)
d being the common difference and f(1) being the first term
for this problem, the equation would be f(n)=10.5(n-1)+10

then to find the first 5 weeks you would plug in 5 for 'n' that is on the right side of the equal sign and solve using PEMDAS

Answer 2

$52 will be my earnings.

Explanation:

My father said that he will pay me $10 for the first week and additional $10.50 will be added each week thereafter.

If the project takes n weeks, total money i earn will be modeled by

Total money = 10 + (n-1)10.50

= 10 + 10.5n - 10.50

= -0.50 + 10.5n

If this project takes 5 weeks then total money earned will be

Total money earned = 10 + (5 - 1)10.50

= 10 + 4×10.50

= 10 + 42

= $52