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Identify the pattern in each sequence and determine the next three elements. Show your work and state the rule.

Mathematics

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Here are the pattern rules and the next three elements for each sequence:

  1. Sequence 1

    The pattern is adding 0.25 to the previous term.
    The next three elements are:
    0.75+0.25=1.000.75 + 0.25 = 1.00
    1.00+0.25=1.251.00 + 0.25 = 1.25
    1.25+0.25=1.501.25 + 0.25 = 1.50
    Rule: Add 0.25. Next three elements: 1.00, 1.25, 1.50\boxed{\text{1.00, 1.25, 1.50}}

  2. Sequence 2

    The pattern is adding 2.50 to the previous term.
    The next three elements are:
    7.50+2.50=10.007.50 + 2.50 = 10.00
    10.00+2.50=12.5010.00 + 2.50 = 12.50
    12.50+2.50=15.0012.50 + 2.50 = 15.00
    Rule: Add 2.50. Next three elements: 10.00, 12.50, 15.00\boxed{\text{10.00, 12.50, 15.00}}

  3. Sequence 3

    The pattern is adding 0.3 to the previous term.
    The next three elements are:
    0.9+0.3=1.20.9 + 0.3 = 1.2
    1.2+0.3=1.51.2 + 0.3 = 1.5
    1.5+0.3=1.81.5 + 0.3 = 1.8
    Rule: Add 0.3. Next three elements: 1.2, 1.5, 1.8\boxed{\text{1.2, 1.5, 1.8}}

  4. Sequence 4

    The pattern is adding 0.15 to the previous term.
    The next three elements are:
    0.45+0.15=0.600.45 + 0.15 = 0.60
    0.60+0.15=0.750.60 + 0.15 = 0.75
    0.75+0.15=0.900.75 + 0.15 = 0.90
    Rule: Add 0.15. Next three elements: 0.60, 0.75, 0.90\boxed{\text{0.60, 0.75, 0.90}}

  5. Sequence 5

    The pattern is adding 0.4 to the previous term.
    The next three elements are:
    1.2+0.4=1.61.2 + 0.4 = 1.6
    1.6+0.4=2.01.6 + 0.4 = 2.0
    2.0+0.4=2.42.0 + 0.4 = 2.4
    Rule: Add 0.4. Next three elements: 1.6, 2.0, 2.4\boxed{\text{1.6, 2.0, 2.4}}

  6. Sequence 6

    The pattern is adding 0.65 to the previous term.
    The next three elements are:
    1.95+0.65=2.601.95 + 0.65 = 2.60
    2.60+0.65=3.252.60 + 0.65 = 3.25
    3.25+0.65=3.903.25 + 0.65 = 3.90
    Rule: Add 0.65. Next three elements: 2.60, 3.25, 3.90\boxed{\text{2.60, 3.25, 3.90}}

  7. Sequence 7

    The pattern is adding 0.2 to the previous term.
    The next three elements are:
    0.6+0.2=0.80.6 + 0.2 = 0.8
    0.8+0.2=1.00.8 + 0.2 = 1.0
    1.0+0.2=1.21.0 + 0.2 = 1.2
    Rule: Add 0.2. Next three elements: 0.8, 1.0, 1.2\boxed{\text{0.8, 1.0, 1.2}}

  8. Sequence 8

    The pattern is adding 2.5 to the previous term.
    The next three elements are:
    7.5+2.5=10.07.5 + 2.5 = 10.0
    10.0+2.5=12.510.0 + 2.5 = 12.5
    12.5+2.5=15.012.5 + 2.5 = 15.0
    Rule: Add 2.5. Next three elements: 10.0, 12.5, 15.0\boxed{\text{10.0, 12.5, 15.0}}

  9. Sequence 9

    The pattern is adding 0.35 to the previous term.
    The next three elements are:
    1.05+0.35=1.401.05 + 0.35 = 1.40
    1.40+0.35=1.751.40 + 0.35 = 1.75
    1.75+0.35=2.101.75 + 0.35 = 2.10
    Rule: Add 0.35. Next three elements: 1.40, 1.75, 2.10\boxed{\text{1.40, 1.75, 2.10}}

  10. Sequence 10

    The pattern is adding 5.5 to the previous term.
    The next three elements are:
    16.5+5.5=22.016.5 + 5.5 = 22.0
    22.0+5.5=27.522.0 + 5.5 = 27.5
    27.5+5.5=33.027.5 + 5.5 = 33.0
    Rule: Add 5.5. Next three elements: 22.0, 27.5, 33.0\boxed{\text{22.0, 27.5, 33.0}}

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