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$1 ; y ; b$ are the first 3 terms of an arithmetic sequence and $1; x ; b$ are the first 3 terms of a geometric sequence. Prove that: $$2y = x^{2} + 1$$
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For arithmetic, y-1=b-y , common difference

for geometric seq, x/1 = b/x , constant ratio

b=x^2

Then subst b into arithmetic, y-1=x^2-y

2y=x^2 + 1  , proven
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