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Consecutive Numbers Investigation
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| Submitted: Thu Jul 11 2002
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James Lucas CONSECUTIVE NUMBERS Problem 1 Gap 1 Take three consecutive numbers; square the middle number, multiply the first by the third number. What do you notice? 2, 3, 4 are consecutive numbers they follow on from each other. The next number is one more than. 2, 3, 4 32 = 3*3 = 9 2*4 = 8 Difference 1 The numbers above are consecutive numbers; the difference between them is one. 18, 19, 20 192 = 19*19 = 361 18*20 = 360 Difference 1 97, 98, 99 982 = 98*98 = 9604 97*99 = 9603 Difference 1 117, 118, 119 1182 = 118*118 = 13924 117*119 = 13923 Difference 1 It appears that it will work every time. I have tried it four times and it works all right so far. I will now try decimals. 1.2, 2.2, 3.2 2.22 = 2.2*2.2 = 4.84 1.2*3.2 = 3.84 Difference 1 10.9, 11.9, 12.9 11.92 = 11.9*11.9 = 141.61 10.9*12.9 = 140.61 Difference 1 It would appear that it works using decimals. I will now try negative numbers. -8, -7, -6 -72 = -7*-7 = 49 -8*-6 = 48 Difference...
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