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Afina-wow [57]
3 years ago
11

What number would complete the pattern? 107 98 90 83 77 68 65

Mathematics
1 answer:
tatiyna3 years ago
8 0
The numbers are part of an arithmetic progression, where the difference between each succeeding number is reduced by 1 each time. Between 107 and 98, the difference is 9. Between 98 and 90, the difference is 8, and so on. This is shown below:

107 - 98 = 9
98 - 90 = 8
90 - 83 = 7
83 - 77 = 6
77 - x = 5
x - 68 = 4
68 - 65 = 3

From that, we can solve for x using either of the equations:

77 - x = 5
x = 77 - 5
x = 72

Therefore 72 would complete the pattern.

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Answer: x = \frac{mn(q - p)}{n-m}\\\\

================================================

Work Shown:

Part 1

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-------------------------------

Explanations:

  • There are quite a bit of steps. I decided to break things into two parts.
  • The goal is to get x all by itself on its own side, which is why I subtracted (x-n)/n from both sides in part 1, step 2. I also subtracted p from both sides.
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