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Question Number 68775 by rajesh4661kumar@gmail.com last updated on 15/Sep/19

Answered by $@ty@m123 last updated on 15/Sep/19

$$Letabethefirsttermanddbethe$$$$commondifferenceofAP.$$$$a+(p-1)d=A...\left(1\right)$$$$a+(q-1)d=AR....\left(2\right)$$$$a+(r-1)d={AR}^2....\left(3\right)$$$$a+(s-1)d={AR}^3....\left(4\right)$$$$\left(1\right)-\left(2\right)$$$$(p-q)d=A-AR$$$$p-q=\frac{A(1-R)}{d}...\left(5\right)$$$$q-r=\frac{AR(1-R)}{d}...\left(6\right)$$$$r-s=\frac{{AR}^2(1-R)}{d}...\left(7\right)$$$$Weobservethat:$$$$\frac{q-r}{p-q}=\frac{r-s}{q-r}=R$$$$Hence,$$$$p-q,q-r,r-sareinG.P.$$

Commented by peter frank last updated on 15/Sep/19

$$thankyou$$

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