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High School Mathematics - 2
3.13 Applications - Arithmetic Sequence/Series

Arithmetic Series:
  • A child's mother gives her 10 cents one day. Everyday thereafter her mother gives 3 more cents than the previous day. After 20 days how much does she have?
    The list of the amounts she gets each day can be written as arithmetic sequence as:
    10, 13, 16, 19, 22..............
    When we add up we get the series:
    10 + 13 + 16 + 19 + 22 + ...................
    Here a = 10, d = 3 and n = 20
    The sum = n/2 (2a + (n-1)d )
    = 20/2 (1(10) + 19(3) )
    = 10 (77)
    = 770
    Answer: 770 cents

  • An auditorium has 20 rows of seats. There are 20 seats in the first row., 21 seats in the second row, 22 seats in the third row, and so on. How many seats are there in all 20 rows?
    The number of seats in the 20 rows form an arithmetic sequence in which the common difference is d = 1
    nth term = a20 = a1 + (n-1)d
    = 20 + 19(1)
    = 20 + 19
    = 39
    Sum of 20 terms is:
    Sn = n/2 (a1 + a20)
    = 20/2 (20 + 39)
    = 10 (59)
    = 590
    Answer: 590

  • Suppose that you play black jack at Harri's on June 1 and lose $1,000. Tomorrow you bet and lose $15 less. Each day you lose $15 less that your previous loss. What will your total losses be for the 30 days of June?
    This is an arithmetic series with a1 = 1000 and d = -15
    We can calculate
    a30 = 1000 - 15(30 - 1) = 565
    Now we use the formula
    S30 = 30/2 (1000 + 565) = 23,475
    You will lose a total of $23,475 during June.
    Answer: $23,475

  • John works for a company and gets a starting salary of $32,500 and annual raise of $1500. Determine the persons salary during the sixth year of employment and the total compensation from the company through 6 full years of employment.
    Answer: $40,000 and $217,500

Directions: Answer the following questions. Also write at least 5 examples of your own.
Q 1: Seating Capacity:
Determine the seating capacity of an auditorium with 30 rows of seats if there are 20 seats in the first row, 24 seats in the second row, 28 seats in the third row, and so on?

Q 2: Seating Capacity: Determine the seating capacity of an auditorium with 36 rows of seats if there are 15 seats in the first row, 18 seats in the second row, 21 seats in the third row and so on.

Q 3: Brick Pattern:
A brick pattern has a approximate shape of a trapezoid. The patio has 18 rows of bricks. The first row has 14 bricks and the 18th row has 31 bricks. How many bricks are in the patio.

Q 4: Number of logs:
Logs are stacked in a pile as shown in the figure. The top row has 15 logs and the bottom row has 21 logs. How many logs are in the stack?

Q 5: Auditorium Seating:
Each row in a small auditorium has two more seats than the preceding row. Find the seating capacity of the auditorium if the front row seats 25 people and there are 15 rows of seats.

Q 6: Baling Hay: In the first two trips around a field baling hay, a farmer makes 93 bales and 89 bales respectively. Because each trip is shorter than the preceding trip, the farmer estimates that the same pattern will continue. Estimate the total number of bales made if there are another six trips around the field.

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