6. In the sequence of positive real numbers $a_{1} 、 a_{2} 、 a_{3} 、 a_{4} 、 a_{5}$, $a_{1} 、$ $a_{2} 、 a_{3}$ form an arithmetic sequence, $a_{2} 、 a_{3} 、 a_{4}$ form a geometric sequence, and the common ratio is not equal to 1. Also, the reciprocals of $a_{3} 、 a_{4} 、 a_{5}$ form an arithmetic sequence. Then ( ).
(A) $a_{1} 、 a_{3} 、 a_{5}$ form a geometric sequence
(B) $a_{1} 、 a_{3} 、 a_{5}$ form an arithmetic sequence
(C) $\frac{1}{a_{1}} 、 \frac{1}{a_{3}} 、 \frac{1}{a_{5}}$ form an arithmetic sequence
(D) $\frac{1}{6 a_{1}} 、 \frac{1}{3 a_{3}} 、 \frac{1}{2 a_{5}}$ form a geometric sequence
6.A.

From the given, we have $\left\{\begin{array}{l}2 a_{2}=a_{1}+a_{3}, \\ a_{3}^{2}=a_{2} a_{4}, \\ a_{3}^{-1}+a_{5}^{-1}=2 a_{4}^{-1} \text {. }\end{array}\right.$
From equation (3), we get $\frac{a_{3}+a_{5}}{a_{3} a_{5}}=\frac{2}{a_{4}}$.
From equation (2), we get $a_{4}=\frac{a_{3}^{2}}{a_{2}}$, substituting this into equation (4), we have
$$
\begin{array}{l}
\frac{a_{3}+a_{5}}{a_{3} a_{5}}=\frac{2 a_{2}}{a_{3}^{2}}=\frac{a_{1}+a_{3}}{a_{3}^{2}} \\
\Rightarrow a_{3}^{2}+a_{3} a_{5}=a_{1} a_{5}+a_{3} a_{5} \\
\Rightarrow a_{3}^{2}=a_{1} a_{5} .
\end{array}
$$