SOLUTION: An auditorium has 50 rows of seats. The first row has 20 seats, the second has 21, each row having 1 more seat than the previous. How many seats are there together? (I figured i

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Question 176989This question is from textbook Mathmatics for Elementary Teachers
: An auditorium has 50 rows of seats. The first row has 20 seats, the second has 21, each row having 1 more seat than the previous. How many seats are there together?
(I figured it out by multiplying 50x20, and then adding the product with the sum of 49+48..., but I do not know a short cut or formula to get the answer)This question is from textbook Mathmatics for Elementary Teachers

Answer by solver91311(12126) (Show Source):
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There are 20 seats in the first row and 20 + 50 - 1 = 69 seats in the last row. You need the sum of the integers from 20 to 69 inclusive.

20 plus 69 = 89

21 plus 68 = 89

and so on

You have 25 (50 divided by 2) such pairs that add to 89, so 25 X 89 = 2225

In general, the sum of a series of integers is where a is the first integer, l is the last integer, and n is the number of integers.