SOLUTION: An auditorium has 20 seats on the first row, 24 seats on the second row, 28 seats on the third row, and so on and has 30 rows of seats. How many seats are in the theatre?

Question 1039326: An auditorium has 20 seats on the first row, 24 seats on the second row, 28 seats on the third row, and so on and has 30 rows of seats. How many seats are in the theatre?

Found 3 solutions by addingup, ikleyn, MathTherapy:
Answer by addingup(3677)   (Show Source): You can put this solution on YOUR website!
20+21+22+23+24+25+26+27+28+29+30 = 275
:
But here is a shortcut to adding consecutive numbers:
Add the smallest number to the largest number of the given set of consecutive numbers. Then multiply the result by the number of numbers in the set. Finally divide the result by two:
:
20+30= 50 and from 20 to 30, BOTH INCLUDED, we have 11 numbers:
50*11 = 550
550/2 = 275
so there you have it.
John
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
An auditorium has 20 seats on the first row, 24 seats on the second row, 28 seats on the third row, and so on and has 30 rows of seats. How many seats are in the theatre?
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For similar problem see the lesson Word problems on arithmetic progressions in this site.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
An auditorium has 20 seats on the first row, 24 seats on the second row, 28 seats on the third row, and so on and has 30 rows of seats. How many seats are in the theatre?

This scenario represents an arithmetic progression (AP), and the formula for the sum of an AP is used: , with:
n, or number in series: 30; , or 1st term: 20, and d, or common difference = 4

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