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Find the rule for the sequence: 8, 9, 15, ...

Mathematics

ScanSolve AI Answer

Step-by-step solution

4 steps

  1. Analyze the given sequence to find the pattern.

    The sequence provided is 8,9,15,…8, 9, 15, \dots

  2. Calculate the differences between consecutive terms.

    The difference between the second and first term is 9−8=19 - 8 = 1.
    The difference between the third and second term is 15−9=615 - 9 = 6.

  3. Calculate the difference between these differences (the second difference).

    The difference between 6 and 1 is 6−1=56 - 1 = 5.

  4. Formulate the rule based on the observed pattern.

    The first differences are 1 and 6. The second difference is 5. Assuming this second difference is constant, the rule is that the amount added to each term to get the next term increases by 5 each time.

    The rule to determine the next number is:

    Add an amount that is 5 greater than the amount added to the previous term.\boxed{\text{Add an amount that is } 5 \text{ greater than the amount added to the previous term.}}
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