B Apply

33. Think About a Plan A meeting room is set up with 16 rows of seats. The number of seats in a row increases by two with each successive row. The first row has 12 seats. What is the total number of seats?
    • How can you find the number of seats in each row using an explicit formula?
    • What is the number of seats in the 16th row?
    • How can you find the sum of the seats in 16 rows?

Determine whether each list is a sequence or a series and finite or infinite.

34. 1, 2, 4, 8, 16, 32, …
35. 1, 0.5, 0.25, 0.125, 0.0625
36. 5 + 10 + ⋯ + 25 5 plus 10 plus math axis ellipsis plus 25
37. − 0.5 − 0.25 − 0.125 − … negative 0.5 minus , 0.25 , minus , 0.125 , minus dot dot dot
38. 4 3 , 7 3 , 10 3 , 13 3 , 16 3 , … 4 thirds , comma , 7 thirds , comma , 10 over 3 , comma , 13 over 3 , comma , 16 over 3 , comma dot dot dot
39. 2.3 + 4.6 + 9.2 + 18.4 2.3 plus 4.6 plus 9.2 plus , 18.4

Each sequence has eight terms. Evaluate each related series.

40. 1 2 , 3 2 , 5 2 , … , 15 2 1 half , comma , 3 halves , comma , 5 halves , comma dot dot dot comma , 15 over 2
41. 1 , − 1 , − 3 , … , − 13 1 comma negative 1 comma . negative 3 comma , dot dot dot comma negative 13
42. 5 , 13 , 21 , … , 61 5 comma 13 comma 21 comma dot dot dot comma 61
43. − 3.5 , − 1.25 , 1 , … , 12.25 negative 3.5 comma negative , 1.25 , comma 1 comma dot dot dot comma , 12.25
44. 1765 , 1414 , 1063 , … , − 692 1765 , comma , 1414 , comma , 1063 , comma dot dot dot comma negative 692
45. − 13 , − 14.5 , − 16 , … , − 23.5 negative 13 comma negative , 14.5 , comma , negative 16 comma , dot dot dot comma negative , 23.5
46. Architecture In a 20-row theater, the number of seats in a row increases by three with each successive row. The first row has 18 seats.
    1. Write an arithmetic series to represent the number of seats in the theater.
    2. Find the total seating capacity of the theater.
    3. Front-row tickets for a concert cost $60. After every 5 rows, the ticket price goes down by $5. What is the total amount of money generated by a full house?
47. 1. Grocery A supermarket displays cans in a triangle. Write an explicit formula for the sequence of the number of cans.
    2. Use summation notation to write the related series for a triangle with 10 cans in the bottom row.
    3. Suppose the triangle had 17 rows. How many cans would be in the 17th row?
    4. Reasoning Could the triangle have 110 cans? 140 cans? Explain.

    

Evaluate each series to the given term.

48. 2 + 4 + 6 + 8 + … ; 2 plus 4 plus 6 plus 8 plus . dot dot dot semicolon  10th term
49. − 5 − 25 − 45 − … ; negative 5 minus 25 minus 45 minus . dot dot dot semicolon  9th term
50. 1. Open-Ended Write two explicit formulas for arithmetic sequences.
    2. Write the first five terms of each related series.
    3. Use summation notation to rewrite each series.
    4. Evaluate each series.

C Challenge

Use the values of a 1 eh sub 1  and S n s sub n  to find the value of a n . eh sub n , .

51. a 1 = 4 eh sub 1 , equals 4  and S 40 = 6080 ; a 40 s sub 40 , equals , 6080 , semicolon , eh sub 40
52. a 1 = − 6 eh sub 1 , equals , minus 6  and S 50 = − 5150 ; a 50 s sub 50 , equals negative , 5150 , semicolon , eh sub 50

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