Sue set up a lemonade stand and sold 10 glasses of lemonade in the first hour of her sales increased at the rate of 20% per hour for the next and hours which function represents the total number of glasses she sold sold in the n hour if the price of one glass of lemonade is $.50 how much money did she earn in the nth hour

This is a geometric sequence because each term is a common ratio of the previous term.  In this case the number of glasses sold in any given hour is 1.2 times the amount sold in the previous hour.  This is a geometric sequenc which can always be expressed as:

a(n)=ar^(n-1), a=initial term, r=common ratio, n=term number.

That is the number of glasses sold in any given hour, n. In this case a=10 and r=1.2 so:

a(n)=10(1.2)^(1-n)

She will earn p*a(n) in any given hour, where p is the price which is 1/2 so her revenue, in dollars, in any given hour will be:

r(n)=5(1.2)^(1-n)