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Complete the following tables

Mathematics

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Step-by-step solution

18 steps

Here are the completed tables:

Part a· 3 steps

  1. Determine the rule for the sequence.

    The values are 5,10,15,205, 10, 15, 20. Each term is 5 times its position.
    The rule is Tn=5nT_n = 5n, where nn is the position and TnT_n is the value of the term.

  2. Find the value of the term for position 5.

    For n=5n=5,

    T5=5×5=25T_5 = 5 \times 5 = 25
  3. Find the position in the sequence for the value of term 40.

    For Tn=40T_n=40,

    5n=405n = 40 n=405=8n = \frac{40}{5} = 8

    The missing values are 25\boxed{\text{25}} for position 5 and 8\boxed{\text{8}} for value 40.

Part b· 3 steps

  1. Determine the rule for the sequence.

    The values are 8,16,24,328, 16, 24, 32. Each term is 8 times its position.
    The rule is Tn=8nT_n = 8n.

  2. Find the value of the term for position 5.

    For n=5n=5,

    T5=8×5=40T_5 = 8 \times 5 = 40
  3. Find the position in the sequence for the value of term 150.

    For Tn=150T_n=150,

    8n=1508n = 150 n=1508=754=18.75n = \frac{150}{8} = \frac{75}{4} = 18.75

    The missing values are 40\boxed{\text{40}} for position 5 and 18.75\boxed{\text{18.75}} for value 150.

Part c· 3 steps

  1. Determine the rule for the sequence.

    The values are 12,24,36,4812, 24, 36, 48. Each term is 12 times its position.
    The rule is Tn=12nT_n = 12n.

  2. Find the value of the term for position 5.

    For n=5n=5,

    T5=12×5=60T_5 = 12 \times 5 = 60
  3. Find the position in the sequence for the value of term 100.

    For Tn=100T_n=100,

    12n=10012n = 100 n=10012=253≈8.33n = \frac{100}{12} = \frac{25}{3} \approx 8.33

    The missing values are 60\boxed{\text{60}} for position 5 and 253 or 8.33\boxed{\frac{25}{3} \text{ or } 8.33} for value 100.

Part d· 3 steps

  1. Determine the rule for the sequence.

    The values are 15,30,45,6015, 30, 45, 60. Each term is 15 times its position.
    The rule is Tn=15nT_n = 15n.

  2. Find the value of the term for position 5.

    For n=5n=5,

    T5=15×5=75T_5 = 15 \times 5 = 75
  3. Find the position in the sequence for the value of term 250.

    For Tn=250T_n=250,

    15n=25015n = 250 n=25015=503≈16.67n = \frac{250}{15} = \frac{50}{3} \approx 16.67

    The missing values are 75\boxed{\text{75}} for position 5 and 503 or 16.67\boxed{\frac{50}{3} \text{ or } 16.67} for value 250.

Part e· 3 steps

  1. Determine the rule for the sequence.

    The values are 3,6,9,123, 6, 9, 12. Each term is 3 times its position.
    The rule is Tn=3nT_n = 3n.

  2. Find the value of the term for position 5.

    For n=5n=5,

    T5=3×5=15T_5 = 3 \times 5 = 15
  3. Find the position in the sequence for the value of term 27.

    For Tn=27T_n=27,

    3n=273n = 27 n=273=9n = \frac{27}{3} = 9

    The missing values are 15\boxed{\text{15}} for position 5 and 9\boxed{\text{9}} for value 27.

Part f· 3 steps

  1. Determine the rule for the sequence.

    The values are 10,20,30,4010, 20, 30, 40. Each term is 10 times its position.
    The rule is Tn=10nT_n = 10n.

  2. Find the value of the term for position 5.

    For n=5n=5,

    T5=10×5=50T_5 = 10 \times 5 = 50
  3. Find the position in the sequence for the value of term 200.

    For Tn=200T_n=200,

    10n=20010n = 200 n=20010=20n = \frac{200}{10} = 20

    The missing values are 50\boxed{\text{50}} for position 5 and 20\boxed{\text{20}} for value 200.

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