... 2074 - 1984 = 90 n th term SIZED DIFFERENCE 1 2 x 2 10 2 3 x 3 40 3 4 x 4 90 I put my results into table and observed that the difference is square number because the box and the grid are square shaped. I predict that for a 5 by 5 square the difference between the products will be 160. 46 47 48 49 50 56 57 58 59 60 66 67 68 69 70 76 77 78 79 80 86 87 88 89 90 46 x 90 = 4140 50 x 86 = 4300 4300 - 4140 = 160 I will now attempt to prove my results algebraically. After doing this I will check my answer using the nxn formula 2x2 square 23 24 33 34 n n+1 n+10 n+11 (24x33)- (23x34) 792-782=10 (n+1) (n+10)-n (n+11) n2 +10n + n+10 - n2 +11n n2 +11n +10 - n2 +11n =10 In both ways the difference is 5x5 square 1 2 3 4 5 11 12 13 14 15 21 22 23 24 25 31 32 33 34 35 41 42 43 44 45 n n+4 n+40 n+44 n (n+44) - [(n+4) (n+40)] (5x41)-(1x45) n2+44n - n2+40n + 4n +160 205-45= 160 n2+44n +160 - n2+44n =160 In ...

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