Question 1163802: Hours before tickets for a rock concert were to
go on sale, people were lined up to buy tickets.
In fact, the first person came 12 hours before
the ticket booth was to open. A new group of
ticket buyers joined the line every 30 minutes.
a. If each new group has two persons more than
the previous group, how many people were
in line after the 20th group joined?
b. How many people were in line 3 hours
before the ticket booth opened?
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! The number of people in each group can be represented by an arithmetic progression, with the first term equal to 1
and the common difference equal to 2.
The nth term of the progression is: a_n = 1 + 2(n-1)
Thus in the 20th group, there are a_20 = 1 + 2(19) = 39 people
The total number of people is the cumulative sum which is given by:
S_n = (n/2)*(a_1 + a_n) -> S_20 = 10*(1 + 39) = 400
3 hours before, there are a total of 2*9 = 18 groups in line
S_18 = 9*(1+35) = 324
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