Respuesta :
The seating capacity of the class that follows an AP is 5180.
What is an arithmetic progression?
An arithmetic progression(AP) is a sequence or series of numbers such that the difference of any two successive members is a constant. The first term is a, the common difference is d, n is number of terms.
For the given situation,
There are 10 seats in the first row, 13 seats in the second row, 16 seats in the third row and so on. There are 56 rows.
This statement follows as Arithmetic Progression.
The series is 10,13,16,.....
Here [tex]a=10, d= 3[/tex]
Number of rows, [tex]n = 56[/tex]
The formula of sum of n terms of an AP is
[tex]S_{n} =\frac{n}{2} [2a+(n-1)d][/tex]
On substituting the above values,
⇒ [tex]S_{56} =\frac{56}{2} [2(10)+(56-1)3][/tex]
⇒ [tex]S_{56} =28 [20+(55)3][/tex]
⇒ [tex]S_{56} =28 [185][/tex]
⇒ [tex]S_{56} =5180[/tex]
Hence we can conclude that the seating capacity of the class that follows an AP is 5180.
Learn more about arithmetic progression here
https://brainly.com/question/20385181
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