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Question Number 81731 by zainal tanjung last updated on 15/Feb/20

$$\mathrm{If}a,b,c\mathrm{are}\mathrm{in}\mathrm{AP};p,q,r\mathrm{are}\mathrm{in}\mathrm{HP}$$$$\mathrm{and}ap,bq,cr\mathrm{are}\mathrm{in}\mathrm{GP},\mathrm{then}\frac{p}{r}+\frac{r}{p}$$$$\mathrm{is}\mathrm{equal}\mathrm{to}$$

Commented by jagoll last updated on 15/Feb/20

$$\left(i\right)a,b,cinAP\Rightarrow 2b=a+c$$$$\left(ii\right)ap,bq,crinGP\Rightarrow {\left(bq\right)}^2=apcr$$$$\left(iii\right)p,q,rinHP\Rightarrow \frac{1}{q}=\frac{2}{\frac{1}{p}+\frac{1}{r}}$$$$\Rightarrow \frac{1}{p}+\frac{1}{r}=2q$$

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