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Find the value of k in the sequence 106, 102, 56, 20, K?

User Cimnine
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Final answer:

To find the value of k in the sequence, differences between terms were analyzed. The pattern of increasing differences by a factor of 42 was discovered, leading to the conclusion that the value of k is 26.

Step-by-step explanation:

The student is tasked with finding the value of k in the sequence 106, 102, 56, 20, k. This is a mathematics problem that requires identifying the pattern of the sequence to determine the next number. To solve this problem, let's first observe the differences between consecutive terms:

  • 102 - 106 = -4
  • 56 - 102 = -46
  • 20 - 56 = -36

Neither the differences are constant (which would indicate an arithmetic sequence) nor do they form a recognizable pattern (such as a geometric sequence).

Let's consider the possibility of a more complex relationship and observe the differences of the differences:

  • -46 - (-4) = -42
  • -36 - (-46) = 10

This reveals that the change from one difference to the next is adding 42. If this pattern continues, we can add 42 to the last difference of -36 to get the next difference.

The next difference would thus be -36 + 42 = 6. Now, to find the next term k, we add this difference to the last known term:

  • 20 + 6 = 26

Therefore, the value of k in the sequence is 26.

User ToJo
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