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I have been given a 10 by 10 grid, with a 2 by 2 box going around numbers 12, 13, 22 and 23, as shown below. I have been asked to find the product of the top right number and the bottom left number in the box (2 by 2 box). Then I was told to do the same with the top left number and the bottom right number. After that I had to calculate the difference between these products. 13 x 22 = 286 _ 12 x 23 = 276 10 By doing this I have decided to investigate further and see what happens with more 2 by 2 squares. 3 by 3 boxes 4 by 4 boxes. 5 by 5 boxes Results: Term (n) 1 2 3 4 5 Differences in opposite corners 0 10 40 90 160 Term (n)...... 1 2 3 4 5 Differences in Opposite corners...... 0 10 40 90 160 10 30 50 70 20 20 20 We know that the nth term will have to be squared. We know this by the second difference is all the same....

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