48. Think About a Plan Suppose a balloon is filled with 5000  cm 3 5000 , cm cubed  of helium. It then loses one fourth of its helium each day. How much helium will be left in the balloon at the start of the tenth day?
    • How can you write a sequence of numbers to represent this situation?
    • Is the sequence arithmetic, geometric, or neither?
    • How can you write a formula for this sequence?
49. Athletics During your first week of training for a marathon, you run a total of 10 miles. You increase the distance you run each week by twenty percent. How many miles do you run during your twelfth week of training?
50. 1. Open-Ended Choose two positive numbers. Find their geometric mean.
    2. Find the common ratio for a geometric sequence that includes the terms from part (a) as its first three terms.
    3. Find the 9th term of the geometric sequence from part (b).
    4. Find the geometric mean of the term from part (c) and the first term of your sequence. What term of the sequence have you just found?

For the geometric sequence 3, 12, 48, 192, …, find the indicated term.

51. 5th term
52. 17th term
53. 20th term
54. nth term

Find the 10th term of each geometric sequence.

55. a 9 = 8 , r = 1 2 eh sub 9 , equals 8 . comma . r equals , 1 half
56. a 9 = − 5 , r = − 1 2 eh sub 9 , equals , minus 5 comma . r equals negative , 1 half
57. a 11 = − 5 , r = − 1 2 eh sub 11 , equals , minus 5 comma . r equals negative , 1 half
58. a 9 = − 1 3 , r = 1 2 eh sub 9 , equals negative , 1 third , comma r equals , 1 half
59. Writing Describe the similarities and differences between a common difference and a common ratio.

C Challenge

60. Banking Copy and complete the table below. Use the geometric mean. Assume compound interest is earned and no withdrawals are made.

    Period 1	Period 2	Period 3
    $140.00	□ white square	$145.64
    $600.00	□ white square	$627.49
    $25.00	□ white square	$32.76
    $57.50	□ white square	$60.37
    $100.00	□ white square	$111.98
    $250.00	□ white square	$276.55

Find a 1 eh sub 1  for a geometric sequence with the given terms.

61. a 5 = 112 eh sub 5 , equals 112  and a 7 = 448 eh sub 7 , equals 448
62. a 9 = 1 2 eh sub 9 , equals , 1 half  and a 12 = 1 16 eh sub 12 , equals , 1 sixteenth

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