A problem on progression If a,b,c are in arithmetic progression., p,q,r in harmonic progression and ap,bq,cr are in geometric progression., then $\frac{p}{r}+\frac{r}{p} = $ ?
EDIT: I have tried to use the basic/standard properties of the respective progressions to get the desired result, but I am not yet successful.

Notice that $\rm\:\ \quad\displaystyle \frac{p}r+\frac{r}p\ =\ \frac{(p+r)^2}{pr} - 2$  
But we have that$\rm\quad\displaystyle p\:r\ =\ \frac{(bq)^2}{ac}\ \ $ via $\rm\ ap,\:bq,\:cr\ $ geometric  
and we have $\rm\quad\ \ \displaystyle p+r\ =\ \frac{2pr}q\quad\ \ \ $ via $\rm\ p,q,r\ $ harmonic
