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jmc

algebra junior

Problem

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 ?

problem
Solution
Since , the common difference in the first column of squares is 4, so the number above 14 is , and the number above 10 is . This is also the fourth number in the row, so the common difference in the row is .

Then the seventh (and last) number in the row is . In the second column, the common difference is , so .
Final answer
-7