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Problem Statement
The problem is to determine the pattern that 4 consecutive odd numbers follows, then subtract the product of the outer two numbers with the product of the inner two numbers.
Plans to Solve/Investigate the Problem My initial plan was to try a few sequences on paper and see what the difference of the products would be to determine if there was a pattern. After that try to determine a procedure to follow to use with excel. Investigation/Exploration of the Problem I first tried the obvious, 3, 5, 7 and 9. (5x7) – (3x9) = 8 then, 23, 25, 27, 29 (25x29)  (23x29) = 8 A pattern for odd consecutive numbers is: (2n +1), (2n +3), (2n +5), (2n+7) Using this for my four consecutive odd numbers and subtracting the products: (2n +3) (2n +5)  (2n +1) (2n+7) 4n^{2 }+ 10n + 6n + 15  4n^{2}  14n  2n  7 = 8, the magic number! Click here to see an excel worksheet for the above problem
Extensions of the Problem If I used 4 consecutive even numbers, the outcome was an eight. A pattern for 4 even consecutive numbers is: (2n +2), (2n +4), (2n +6) (2n+8) (2n +4) (2n+6) – (2n +2) (2n +8) 4n^{2 }+ 12n + 8n + 24  4n^{2}  16n  4n  16 = 8 Click here to see an excel worksheet for the above problem. Author & Contact



