Question

A theater seats 2,816 people. The first row has 26 seats while the last row has 150 seats. Assuming the number of seats per row follows an arithmetic sequence,

how many rows does the theater have?

Answer 1

The theater has 32 rows

Explanation:

The rule of the sum of n terms of an arithmetic sequence is S
`_(n)` =
`(n)/(2)` (a + l), where

• a is the first term

• l is the last term

• n is the number of the terms

∵ The number of seats per row follows an arithmetic sequence

∵ The first row has 26 seats

∴ a = 26

∵ The last row has 150 seats

∴ l = 150

∵ The theater seats are 2,816

∴ S
`_(n)` = 2,816

→ Substitute these values in the rule of the sum above to find n

∵ 2,816 =
`(n)/(2)`(26 + 150)

∴ 2,816 =
`(n)/(2)`(176)

∴ 2,816 = 88n

→ Divide both sides by 88

∴ 32 = n

∵ n represents the number of the rows

∴ The theater has 32 rows