SOLUTION: a theater has 20 rows of chairs the first row has 10 chairs and each row after that has 2 more seats than the row before it How many total seats are in the theater

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Question 1206130: a theater has 20 rows of chairs the first row has 10 chairs and each row after that has 2 more seats than the row before it
How many total seats are in the theater
Answer by ikleyn(52790) About Me  (Show Source):
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a theater has 20 rows of chairs the first row has 10 chairs and each row after that
has 2 more seats than the row before it. How many total seats are in the theater?
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The series of the chairs in rows is an arithmetic progression.


1-st row has 10 chairs.

The last, 20th row has 10 + (20-1)*2 = 10 + 19*2 = 10 + 38 = 48 chairs.

(use the formula for the n-th term of an AP).



In all, there are  %28%28a%5B1%5D%2Ba%5B20%5D%29%2F2%29%2A20 = %28%2810%2B48%29%2F2%29%2A20 = %2858%2F2%29%2A20 = 58*10 = 580 chairs.

(use the formula for the sum of the first n terms of an AP).

Solved.

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For introductory lessons on arithmetic progressions see
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.