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?

The theater has 32 rows

Step-by-step explanation:

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

∵ 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 = 2,816

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

∵ 2,816 = (26 + 150)

∴ 2,816 = (176)

∴ 2,816 = 88n

→ Divide both sides by 88

∴ 32 = n

∵ n represents the number of the rows

∴ The theater has 32 rows

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98