432, 456, 576, 786, what comes next in the sequence

General
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432, 456, 576, 786, what comes next in the sequence

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432, 456, 576, 786, what comes next in the sequence?

To determine the next number in the sequence 432, 456, 576, 786, it’s important to first look for a pattern. We can analyze the sequence step-by-step:

  1. Calculate the differences between the consecutive terms:

    • ( 456 - 432 = 24 )
    • ( 576 - 456 = 120 )
    • ( 786 - 576 = 210 )

  2. Analyze the differences:

    • First difference: 24
    • Second difference: 120
    • Third difference: 210

  3. Find a pattern in the differences:
    Upon further inspection, it seems that the differences themselves do not follow an immediately obvious arithmetic or geometric pattern. However, let’s check if there is a pattern in the way differences are increasing.

  4. Pattern in differences:

    • ( 120 - 24 = 96 )
    • ( 210 - 120 = 90 )

  5. Second-order differences (differences of the differences):

    • ( 120 - 24 = 96 )
    • ( 210 - 120 = 90 )

    The second-order differences are themselves decreasing by 6:

    • ( 126 - 90 = 96 )

  6. Predicting the next difference:
    If the pattern of the second-order differences continues to decrease by 6:

    • The next difference in the differences would likely be: ( 210 + (90 - 6) = 210 + 84 = 294 )

  7. Calculating the next term in the sequence:

    • The next term should be ( 786 + 294 = 1080 )

Therefore, the next number in the sequence is 1080.