Answer :
The number of seats in the theater is 1510.
Here we have to find the number of seats in the theater.
Data given:
Total row = 20
number of seats on the first row = 28
number of seats on the second row = 33
number of seats on the third row = 38
Therefore we get the series as 28, 33, 38......., which is in arithmetic sequence.
The common difference (d) = 5
Here we have to find the sum of the series.
The formula for the sum of n term of the arithmetic sequence:
[tex]S_{n}[/tex] = n/2( 2a + (n-1)d)
= 20/2 ( 2× 28 + (20 -1) 5)
= 10 ( 56 + 19×5)
= 10( 56 + 95)
= 10 ×151
= 1510
Therefore the number of seats is 1510.
To know more about the arithmetic sequence refer to the link given below:
https://brainly.com/question/6561461
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