Question

In an auditorium, there are 22 seats in the first row, and 28 seats in the second row. The number of seats in a row, n, continues to increase by 6 with each additional row.

Which row will have 100 seats?

Row #
has 100 seats.

Answer 1

12

Explanation:

Answer 2

The nth row will have 100 seats when:

100 = 22 + (n-1)*6

Simplifying the equation gives:

n = 14.67

Since rows cannot have fractional values, the 15th row will have 100 seats

Explanation:

To solve this problem, we can use the formula for the arithmetic sequence, which is:

an = a1 + (n-1)d

where:

an = the nth term

a1 = the first term

d = the common difference between terms

n = the number of terms

In this problem, the first row has 22 seats, and the second row has 28 seats. The common difference between the number of seats in adjacent rows is 6, since the number of seats increases by 6 with each additional row. Therefore, we can write the formula for the number of seats in the nth row as:

an = 22 + (n-1)6

We want to find the row that has 100 seats, so we can set an equal to 100 and solve for n:

100 = 22 + (n-1)6

Simplifying this equation gives:

78 = 6n - 6

Adding 6 to both sides and dividing by 6 gives:

n = 14.67

However, since rows cannot have fractional values, we round up to the nearest whole number to get:

n = 15

Therefore, the 15th row will have 100 seats.