If a, b and c are in continued proportion, then a2 :  b2 isA a2 :  c2 B a : b C a : c D b : c

Break Down the Problem

1. Identify the relationship between $a$, $b$, and $c$ in the continued proportion.
2. Establish the ratio $a^2 : b^2$ in terms of $a$, $b$, and $c$.

Relevant Concepts

1. From the property of continued proportion, we have: $\frac{a}{b} = \frac{b}{c}$ which can be rewritten as: $b^2 = ac$

Analysis and Detail

1. We need to express $a^2 : b^2$: $\frac{a^2}{b^2} = \frac{a^2}{ac} = \frac{a^2}{b^2} = \frac{a^2}{\sqrt{ac}^2}$
2. We have: $b = \sqrt{ac}$
3. Now, let's derive the ratios: $\frac{a^2}{b^2} = \frac{a^2}{ac} = \frac{a}{c}$

Verify and Summarize

1. The verification leads us to realize: $\frac{a^2}{b^2} = \frac{a}{c}$ implies that $a^2 : b^2 = a : c$.

Final Answer

The ratio $a^2 : b^2$ is $a : c$, which corresponds to option C.