el diseño de un teatro consta de 27 sillas en la primera fila , 32 en la segunda, 37 en la tercera y asi sucesivamente. se sabe que el teatro tiene 10 filas. ¿ cuantas sillas tiene el teatro?

Alyce Wilkinson 2021-02-08 Answered
el diseño de un teatro consta de 27 sillas en la primera fila , 32 en la segunda, 37 en la tercera y asi sucesivamente. se sabe que el teatro tiene 10 filas.
¿ cuantas sillas tiene el teatro?
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Answers (1)

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Answered 2022-04-04 Author has 208 answers

The number of chairs in each row is represented by the sequence 27, 32, 37, ....
The total number of chairs is then represented by the series 27, 32, 37, ....
Since 3227=5 and 3732=5, then the number of chairs in each row is represented by an arithmetic sequence with a first term of a1=27 and a a common difference of d=5.
The total number of chairs will then be found using the partial arithmetic sum formula Sn=n(a1+an)2​. It is given that the theater has 10 rows so n=10. To use this formula when n=10, you must then find a10.
The nnth term of an arithmetic sequence is an=a1+(n1)d. Therefore:
a10
=27+(101)(5)
=27+9(5)
=27+45
=72
The total number of chairs is then:
Sn=n(a1+an)2 Partial sum formula.
S10=10(27+72)2 Substitute n=10,a1=27 and a10=72
=5(99)
495
The theater then has 495 chairs.

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