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Given each sequence below identify the level of difference

.a.) 0, 12, 10, 0, -12, -20
b.) 1, 4, 8, 13, 19, 26

User Tpschmidt
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1 Answer

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Final answer:

The first sequence has no consistent first or second-level difference, indicating it is neither an arithmetic nor a quadratic sequence. The second sequence has a consistent first-level difference that increases by 1, suggesting a possible quadratic pattern.

Step-by-step explanation:

To identify the level of difference in a sequence, we calculate the differences between consecutive terms until we find a consistent pattern. Let's analyze each sequence provided:

Sequence a) 0, 12, 10, 0, -12, -20

Differences between terms:

  • 12 - 0 = 12
  • 10 - 12 = -2
  • 0 - 10 = -10
  • -12 - 0 = -12

-20 - (-12) = -8
Since there is no consistent pattern in the first set of differences, let's calculate the second set of differences to check for a second-level pattern:

  • -2 - 12 = -14
  • -10 - (-2) = -8
  • -12 - (-10) = -2
  • -8 - (-12) = 4

The second set of differences also does not show a pattern, indicating this sequence does not have a common difference (i.e., it is not an arithmetic sequence), nor does it show a consistent second-level difference (i.e., it is not a quadratic sequence).

Sequence b) 1, 4, 8, 13, 19, 26

Differences between terms:

  • 4 - 1 = 3
  • 8 - 4 = 4
  • 13 - 8 = 5
  • 19 - 13 = 6
  • 26 - 19 = 7
    The differences here are consistent and increase by 1 each time, indicating a

first-level difference. This pattern suggests the presence of a polynomial of degree higher than 1, possibly a quadratic pattern.

User Zuku
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