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At the start of summer, Miguel's 2500 L water reservoir is completely filled. He uses 150 L of water every week for his plants.
a. Calculate how much water remains in the reservoir after 1, 2, 3, and 4 weeks.
b. Explain why the amount of water left in the reservoir after $n$ weeks forms an arithmetic sequence.
c. Determine the number of weeks it will take for Miguel's reservoir to be empty.
544
513
552
A movie theater arranges its seating in rows following an arithmetic sequence. In the fifth row, there are 18 seats, and in the tenth row, there are 28 seats.
(a) What is the common difference in the number of seats between each row?
The theater has a total of 15 rows, and there are 10 seats in the first row.
(b) How many seats are there in total across all rows in the theater?
595
542
516
Mark is making orange juice. After squeezing 8 oranges, he has gathered 365.6 mL of juice.
(a) Calculate the average amount of juice he gets from each orange.
(b) Based on this average, create an arithmetic sequence $v_n$ that represents the total amount of juice collected from squeezing n oranges.
(c) Estimate the total amount of juice collected from squeezing 15 oranges.
512
566
524
In a theater, the seats are arranged in rows following an arithmetic sequence. There are 22 seats in the fifth row and 52 seats in the tenth row.
(i) What is the common difference, $d$, of this arithmetic sequence?
(ii) What is the number of seats in the first row of this sequence?
520
548
580
