Problem

At a certain concert, the audience was allowed to enter in a certain way. The first time a...

At a certain concert, the audience was allowed to enter in a certain way. The first time a bell rang only 1 person was allowed to enter and choose his or her seat. The second time the bell rang 3 people were allowed to enter. On each successive ring the group that enters has two more people than the previous group.

a. How many people have entered after the 25th ring of the bell?


b. How many have entered after the nth ring?


c. After how many rings will there be at least 1000 people?

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