Your father wants you to 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.

$52 will be my earnings.

Step-by-step 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

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺