How Do You Calculate Total Seats in a Concert Hall with Increasing Row Sizes?

[Blueshy]

Increasing Row Size...

Homework Statement

There are 150 rows at a concert hall. Each row you move back there is an increase of 10% in the number of seats. The first row has 100 seats. How many seats are there in the concert hall?

Homework Equations

I don't know the equation to represent this change.

The Attempt at a Solution

Obviously I could go through and do each rows amount of seats, but I'd like to know the equation that will solve this. Is it n(n+1)/2?

 

[Dick]

It's called a geometric series. The number of seats in the nth row is 100*(1.1)^n (where n=0 is the first row). Now find a reference and look for 'geometric series'.

 

[dynamicsolo]

Homework Statement

There are 150 rows at a concert hall. Each row you move back there is an increase of 10% in the number of seats. The first row has 100 seats. How many seats are there in the concert hall?

Notice that the number of seats in each successive row increases by a constant proportion, that is, each row has 1.10 times as many seats as the preceding row. What kind of a sequence is this?

If you have to add a finite number of terms of a sequence of this type, what formula do you use?