Respuesta :
Using an arithmetic sequence, it is found that the opera house will have 6150 chairs.
What is an arithmetic sequence?
In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
The sum of the first n terms is given by:
[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]
In this problem, the sequence is:
[tex]t_n = 25 + 4(n - 1)[/tex]
Hence the first term and the common ratio are given, respectively, by:
[tex]a_1 = 25, d = 4[/tex]
Then the 50th term is:
[tex]t_{50} = 25 + (50 - 1) \times 4 = 221[/tex]
The number of chairs is the sum of the first 50 terms, hence:
[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]
[tex]S_n = 25(25 + 221) = 6150[/tex]
More can be learned about arithmetic sequences at https://brainly.com/question/6561461
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