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The sequence of integers in the row of squares and in each of the two columns of squares form three distinct arithmetic sequences. What is the value of $N$?

 

 


 

 Feb 21, 2021
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The first vertical column can be filled from the bottom: 18, 14, 10, 6.

 

In the horizontal row, we have 21, ___, ___, 6. The common difference of this is 5, so we can fill that in: 21, 16, 11, 6, 1, -4, -9.

 

Finally, we have the vertical column to the right. From the bottom, the numbers are -17, __, __, __, -9, N. The common difference is 2, so N = -7

 Feb 21, 2021

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