SOLUTION: A concert hall has 100 seats in the first row, 102 seats in the second row, 104 in the third row, and so on. The last row has 168 seats. a) how many total rows does the concert h

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Question 987848: A concert hall has 100 seats in the first row, 102 seats in the second row, 104 in the third row, and so on. The last row has 168 seats.
a) how many total rows does the concert hall have?
B) how many seats does the concert hall have?
Answer by ikleyn(52801) About Me  (Show Source):
You can put this solution on YOUR website!
.
This is an arithmetic progression with the first term 100 and the common difference 2.  The last term is  168.

The number of rows is  %28168-100%29%2F2+%2B+1 = 68%2F2+%2B+1 = 34 + 1 = 35.
It is also the number of terms of the progression.

Now,  use the formula for the sum of first  n  terms of an arithmetic progression.  See,  for example, the lesson  Arithmetic progressions  in this site.

S = %28%28a%5B1%5D%2Ba%5Bn%5D%29%2F2%29.n = %28100%2B168%29%2F2.35 = 268%2F2.35 = 134*35 = 4690.

The number of seats in the concert hall is 4690.

For more word problems on arithmetic progression see the lesson  Word problems on arithmetic progressions  in this site.