SOLUTION: Rina will hold her piano recital at the music hall of her school. The music hall has 12 rows of seats, in which the first row has 15 seats. Each succeeding row has 3 more seats tha

Question 1039333: Rina will hold her piano recital at the music hall of her school. The music hall has 12 rows of seats, in which the first row has 15 seats. Each succeeding row has 3 more seats than the one in front of it. What is the maximum number of people who can be seated in the music hall?
Found 4 solutions by ankor@dixie-net.com, josmiceli, MathTherapy, ikleyn:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
Rina will hold her piano recital at the music hall of her school.
The music hall has 12 rows of seats, in which the first row has 15 seats.
Each succeeding row has 3 more seats than the one in front of it.
What is the maximum number of people who can be seated in the music hall?
:
I know there should be a more elegant way to do this, but all I can come up with is :
15 + 18 + 21 + 24 + 27 + 30 + 33 + 36 + 39 + 42 + 45 + 48 = 378 max people
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
The sequence for the rows is:

etc.
-----------------
If you have rows, the sum would be:
15*n + 3*( 1 + 2 + 3 + . . . + (n-1) )
------------------------------
If and , you
can use a formula for the sum of the digits:

The maximum number of people who
can be seated is 246
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Rina will hold her piano recital at the music hall of her school. The music hall has 12 rows of seats, in which the first row has 15 seats. Each succeeding row has 3 more seats than the one in front of it. What is the maximum number of people who can be seated in the music hall?

This scenario represents an arithmetic progression (AP), and the formula for the sum of an AP is used: , with:
n, or number in series: 12; , or 1st term: 15, and d, or common difference = 3

Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
For similar problem see the lesson Word problems on arithmetic progressions in this site.

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