If a, b and c are in continued proportion, prove that b² = ac, and hence find b when a = 8 and c = 18 with b positive.

b² = ac follows from a : b = b : c, and b = 12.

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Explanation

Continued proportion means a : b = b : c, so b × b = a × c, that is b² = ac. With a = 8 and c = 18, b² = 144 and the positive value is b = 12.