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1. In a concert hall, the number of seats in each row increases as you move farther from the stage. There are
the first row, 38 seats in the second row, and 45 seats in the third row.
a) If this pattern continues, determine what type of sequence this represents. Then write a function rule in simplified
form that can be used to find the number of seats in the nth row. Be sure to use the correct notation you have
learned this unit. Show ALL work.
b) Use the rule to determine which row has 290 seats. Show ALL work.

1 In a concert hall the number of seats in each row increases as you move farther from the stage There are the first row 38 seats in the second row and 45 seats class=

Respuesta :

According to the situation described, we have that:

a) The arithmetic sequence that gives the number of seats in the nth row is given by:

[tex]a_n = 24 + 7n[/tex]

b) The 38th row has 290 seats.

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]

Item a:

The first row has 31 seats, the second has 38, the third has 45 and so on, hence:

  • It is an arithmetic sequence.
  • The common difference is d = 7.
  • The first term is [tex]a_1 = 31[/tex].

Then, the rule is:

[tex]a_n = a_1 + (n - 1)d[/tex]

[tex]a_n = 31 + 7(n - 1)[/tex]

[tex]a_n = 24 + 7n[/tex]

Item b:

This is the nth row, for which [tex]a_n = 290[/tex], hence:

[tex]a_n = 24 + 7n[/tex]

[tex]290 = 24 + 7n[/tex]

[tex]7n = 266[/tex]

[tex]n = \frac{266}{7}[/tex]

[tex]n = 38[/tex]

The 38th row has 290 seats.

You can learn more about arithmetic sequences at https://brainly.com/question/26366645

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