Discussion
If the 3rd, 7th, 11th terms of a geometric progression are a, b, c respectively, then \((ac)^{4} =\)
Answer: A
\((ac)^{4}\) equals \(b^{8}\).
The 3rd, 7th and 11th terms are equally spaced (four steps apart), so they themselves form a G.P., and the middle one is the geometric mean of the other two.
\[ \begin{aligned} a &= Ar^{2},\ b = Ar^{6},\ c = Ar^{10} \\ ac &= A^{2}r^{12} = b^{2} \\ (ac)^{4} &= b^{8} \end{aligned} \]
\(b^{4}\) is \((ac)^{2}\), and \(b^{2}\) is ac itself, so those options stop a step short.
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