Yesterday you borrowed $30 from your brother. every day that you don't pay it back, you owe $2.00 more. so today, day 1, you owe him $32.00; on day 2 you will owe him $34.00; on day 3 you will owe him $36.00, etc. if you still haven't paid him back, how much will you owe him on day 22?

Since the amount of increase in debt has a constant value, therefore this follows an arithmetic series which has a general form of:

an = a1 + (n - 1) d

where the variables are,

an = is the amount at specified time or days n

a1 = the initial amount of debt = 30

n = time in days = 22

d = common difference = 2

Therefore calculating for the amount owed after 22 days:

an = 30 + (22 - 1) * 2

an = 30 + 42

an = $ 72

Therefore the amount owed after 22 days is 72 dollars.