A concert hall has the following numbers of seats in the first 5 rows.
18 seats in row 1
21 seats in row 2
24 seats in row 3
27 seats in row 4
30 seats in row 5
As the row number increases, the number of seats continues to follow the same pattern, resulting in an arithmetic sequence. Which explicit formula gives the terms of this sequence?
The explicit formula for this arithmetic sequence can be written as:
an = 15 + 3(n-1)
where:
an = number of seats in row n
n = row number
So, for example, to find the number of seats in row 10:
a10 = 15 + 3(10-1)
a10 = 15 + 3(9)
a10 = 15 + 27
a10 = 42
Therefore, there would be 42 seats in row 10 of the concert hall.