A concert is held in a stadium with stadium seating. there are 25 seats in the first row, 27 seats in the second row, 29 seats in the third row and so on. there are 200 rows. what is the seating capacity of the stadium?

Question

Arjun Crosby

Mathematics

12 April, 01:33

A concert is held in a stadium with stadium seating. there are 25 seats in the first row, 27 seats in the second row, 29 seats in the third row and so on. there are 200 rows. what is the seating capacity of the stadium?

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Rayan · Answer 1

Alright, so let's make a function for the number of seats in a row. Number of seats = 25 + (number of row-1) (2) because it goes up by two. We start with 25, so we have that, then we get that it adds by 2 every row. However, for the first row it only has 25, so we have the number of the row - 1. If we figure out the 200th row, we get 25+398=423. Adding that and 25, we get 448. 448*100=44800, and we get that number because with an even number of rows, we add the 1st and 200th, the 2nd and 99th, and so on. This works because as you go up rows, you add two, and as you decrease rows, you decrease by two, so they cancel each other out and form 100 pairs. All pairs are equal.