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There are several patterns in the grid, depending on whether you look by row or by column. Within each row, there are positive and negative terms at the beginning that cancel each other. For example, in the first row, you have –2 + 2 = 0 and –1 + 1 = 0. The only terms in the first row that contribute to the sum are 3 and 4, in the far-right columns. The same is true for the other rows.
Thus, the sum of the grid is equal to the sum of only the two far-right columns. The sum in the first row in those columns is 3 + 4 = 7; the sum in the next row is 6 + 8 = 14, etc. The sum in the final row is 18 + 24 = 42. Add 7 + 14 + 21 + 28 + 35 + 42 in your calculator to get 147.