Question

1. In a concert hall, the number of seats in each row increases as you move farther from the stage. There are

Answer 1

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:

$a_n = 24 + 7n$

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:

$a_n = a_1 + (n - 1)d$

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 $a_1 = 31$.

Then, the rule is:

$a_n = a_1 + (n - 1)d$

$a_n = 31 + 7(n - 1)$

$a_n = 24 + 7n$

Item b:

This is the nth row, for which $a_n = 290$, hence:

$a_n = 24 + 7n$

$290 = 24 + 7n$

$7n = 266$

$n = \frac{266}{7}$

$n = 38$

The 38th row has 290 seats.

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