Question 1109379
2, 6, 12, 20
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first level differences are
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4, 6, 8
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second level differences are
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2, 2
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therefore we know the formula is a quadratic of the form
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an^2 +bn + c
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for n=1, we have a +b +c = 2
for n=2, we have 4a +2b +c = 6
for n=3, we have 9a +3b +c = 12
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we have a system of three equations in three unknowns
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subtract the first equation from the second and third equations
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3a +b = 4
8a +2b = 10
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using the first one, solve for b and substitute in the second one
b = 4-3a
8a +2(4-3a) = 10
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8a +8 -6a = 10
2a = 2
a = 1
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substitute for a in 3a +b = 4
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3(1) + b = 4
b = 1
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a = 1 and b = 1, therefore
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c = 0
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our formula is n^2 +n
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x(12) = 12^2 + 12 = 156
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you are correct
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