The sequence a,1,b is a non-constant arithmetic progression. The sequence 1,a,b is a geometric progression. Find b.
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Since a,1,b is an arithmetic progression, a+b=2, therefore b=2−a. By the geometric progression\'s property, we get a2=b=2−a a2+a−2=0: a1=1 or a2=−2. But the arithmetic progression is non-constant, therefore a≠1, so a must be -2. b=2−a=2−(−2)=4.