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A sequence is defined by the rule that the value of the nth term is n multiplied by a constant. Complete the following tables:

Mathematics

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Answers

6 parts
a

200\text{200}

b

84\text{84}

c

128\text{128}

d

1200\text{1200}

e

450\text{450}

f

125000\text{125000}

Step-by-step solution

12 steps

Here are the completed tables:

Part a· 2 steps

  1. Identify the pattern.

    The values of the terms are 10, 20, 30, 40. This is an arithmetic sequence where each term is the position multiplied by 10.
    Pattern: Value of term = Position ×\times 10.

  2. Calculate the missing value for position 20.

    Value of term for position 20 = 20×10=20020 \times 10 = 200.
    The missing value is 200\boxed{\text{200}}.

Part b

84\text{84}

  1. Identify the pattern.

    The values of the terms are 3, 6, 9, 12. This is an arithmetic sequence where each term is the position multiplied by 3.
    Pattern: Value of term = Position ×\times 3.

  2. Calculate the missing value for position 28.

    Value of term for position 28 = 28×3=8428 \times 3 = 84.
    The missing value is 84\boxed{\text{84}}.

Part c

128\text{128}

  1. Identify the pattern.

    The values of the terms are 8, 16, 24, 32. This is an arithmetic sequence where each term is the position multiplied by 8.
    Pattern: Value of term = Position ×\times 8.

  2. Calculate the missing value for position 16.

    Value of term for position 16 = 16×8=12816 \times 8 = 128.
    The missing value is 128\boxed{\text{128}}.

Part d

1200\text{1200}

  1. Identify the pattern.

    The values of the terms are 12, 24, 36, 48. This is an arithmetic sequence where each term is the position multiplied by 12.
    Pattern: Value of term = Position ×\times 12.

  2. Calculate the missing value for position 100.

    Value of term for position 100 = 100×12=1200100 \times 12 = 1200.
    The missing value is 1200\boxed{\text{1200}}.

Part e

450\text{450}

  1. Identify the pattern.

    The values of the terms are 15, 30, 45, 60. This is an arithmetic sequence where each term is the position multiplied by 15.
    Pattern: Value of term = Position ×\times 15.

  2. Calculate the missing value for position 30.

    Value of term for position 30 = 30×15=45030 \times 15 = 450.
    The missing value is 450\boxed{\text{450}}.

Part f

125000\text{125000}

  1. Identify the pattern.

    The values of the terms are 1, 8, 27, 64. These are perfect cubes.
    1=131 = 1^3
    8=238 = 2^3
    27=3327 = 3^3
    64=4364 = 4^3
    Pattern: Value of term = Position3^3.

  2. Calculate the missing value for position 50.

    Value of term for position 50 = 503=50×50×50=12500050^3 = 50 \times 50 \times 50 = 125000.
    The missing value is 125000\boxed{\text{125000}}.

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