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Describe the pattern in the sequence: 8, 9, 15, ...

Mathematics

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Step-by-step solution

3 steps
  1. Recall the sequence and the differences calculated previously.

    The sequence is 8,9,15,…8, 9, 15, \dots.
    The difference between the first two terms is 9−8=19 - 8 = 1.
    The difference between the second and third terms is 15−9=615 - 9 = 6.

  2. Describe the pattern of these differences.

    The amount added to each term to get the next term is increasing. The increase in the amount added is 6−1=56 - 1 = 5.

  3. Formulate the description in words.

    The pattern starts with 8. To get the next term, an increasing amount is added. The amount added increases by 5 each time. For example, 1 is added to 8 to get 9, and then 1+5=61+5=6 is added to 9 to get 15.

    The pattern increases by adding a value that is 5 greater than the value added to the previous term.\boxed{\text{The pattern increases by adding a value that is } 5 \text{ greater than the value added to the previous term.}}
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