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12 #36 Saver

12 #36 Saver
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12 x 14 x 55 36 Knotless Batting Cage Net w Free Shipping and Free Net Saver
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12 x 12 x 70 36 Batting Cage Net w Free Net Saver
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12 #36 Saver
BE A 'LIFE SAVER' GUYS - METHOD OF DIFFERENCES! (m.o.d)?

Hi guys, any chance you lovely people can stop me being confused about this method of differences? x x

N 1 2 3 4 5 6 7
Un - 2, 8, 26, 62, 122, 212, 338
D1 - 6, 18, 36, 60, 90, 126,
D2 - 12, 18, 24, 30, 26
D3 - 6, 6, 6, 6, 6

As D3 is constant, the highest power is n3 which means that Un = An3 + Bn2 + Cn + D

N = 1 (Un = 1A + 1B + 1C + D = 2) Line 1
N= 2 (Un = 8A + 4B + 2C + D = 8) Line 2
N = 3 (Un = 27A + 9B + 3C + D = 26) Line 3
N = 4 (Un= 64A + 16B + 4C + D = 22) Line 4

Line 2 - Line 1 (7A + 3B + C = 6) Now Line 5
Line 3 - Line 2 (19A + 5B + C = 18) Now Line 6
Line 4 - Line 3 (37A + 7B + C = 36) Now Line 7

Line 6 - Line 5 (12A + 2B = 12) Now Line 8
Line 7 - Line 6 (18A + 2B = 18) Now Line 9

Line 9 - Line 8 (6A = 6, A = 6/6 = 1)

PLEASE GUYS CAN YOU TELL ME - NOW I'VE WORKED OUT A, HOW TO WORK OUT THE VALUES OF B, C AND (THE ONE I'M MOST CONFUSED ABOUT) D?

THANKS x x

Pick one of the equations in A and B, say, 12A + 2B = 12
and substitute the value of 1 for A, so, 12*1 + 2B = 12 implies B = 0.

Then substitute the values for A and B into one of the equations
you already have in A, B and C, say, 7A + 3B + C = 6.
7*1 + 3*0 + C = 6, so C = -1.

Then use, say, A + B + C + D = 2 as your next equation for substitution.
1 + 0 - 1 + D = 2, so D = 2.

Final equation is : Un = n^3 - n + 2

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