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Growing Squares
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| Submitted: Sun Aug 03 2003
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Growing Squares I have decided to find a formula to find the nth term. To help me find the nth term I shall compose a table including all the results I know. Pattern Number Number of Squares 1st Difference 2nd Difference 1 1 4 4 2 5 8 3 13 4 12 4 25 The 2nd difference is constant; therefore the equations will be quadratic. The general formula for a quadratic equation is an2 + bn +c. The coefficient of n2 is half that of the second difference Therefore so far my formula is: 2n2 + [extra bit] I will now attempt to find the extra bit for this formula. Pattern Number Extra Bit 1st Difference 2nd Difference 1 2 6 4 2 8 10 3 18 4 14 4 32 From my table of results I have found the formula to be 2n2 + 2n + 1 I will now check my formula by substituting a value from the table in to my formula: E.g. n = 2 Un = 2 (2) 2 - 2 (2) + 1 = 8. For Diagrams 1 - 4 I can see a pattern with...
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