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What is the pattern in each sequence? a) 18, 25, 32, ... b) -13, -6, 1, 8, ... c) 104, 107, 110, 113, ... d) -17, -14, -11, ...

Mathematics

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Step-by-step solution

12 steps

Here are the descriptions for each pattern:

Part a· 3 steps

  1. Observe the starting point and the first jump.

    The pattern starts at 18 and jumps to 25.

  2. Calculate the difference between the numbers.

    25−18=725 - 18 = 7
  3. Verify with the next jump.

    The next jump is from 25 to 32.

    32−25=732 - 25 = 7

    The pattern is adding 7 to the previous number.

Part b· 3 steps

  1. Observe the starting point and the first jump.

    The pattern starts at −13-13 and jumps to −6-6.

  2. Calculate the difference between the numbers.

    −6−(−13)=−6+13=7-6 - (-13) = -6 + 13 = 7
  3. Verify with the next jumps.

    The next jump is from −6-6 to 1: 1−(−6)=1+6=71 - (-6) = 1 + 6 = 7.
    The next jump is from 1 to 8: 8−1=78 - 1 = 7.
    The pattern is adding 7 to the previous number.

Part c· 3 steps

  1. Observe the starting point and the first jump.

    The pattern starts at 104 and jumps to 107.

  2. Calculate the difference between the numbers.

    107−104=3107 - 104 = 3
  3. Verify with the next jumps.

    The next jump is from 107 to 110: 110−107=3110 - 107 = 3.
    The next jump is from 110 to 113: 113−110=3113 - 110 = 3.
    The pattern is adding 3 to the previous number.

Part d· 3 steps

  1. Observe the starting point and the first jump.

    The pattern starts at −17-17 and jumps to −14-14.

  2. Calculate the difference between the numbers.

    −14−(−17)=−14+17=3-14 - (-17) = -14 + 17 = 3
  3. Verify with the next jumps.

    The next jump is from −14-14 to −11-11: −11−(−14)=−11+14=3-11 - (-14) = -11 + 14 = 3.
    The next jump is from −11-11 to −8-8: −8−(−11)=−8+11=3-8 - (-11) = -8 + 11 = 3.
    The pattern is adding 3 to the previous number.

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