If-a-b-c-are-in-AP-p-q-r-are-in-HP-and-ap-bq-cr-are-in-GP-then-p-r-r-p-is-equal-to-

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

If a, b, c are in AP; p, q, r are in HP

and a p, b q, c r are in GP, then \frac{p}{r} + \frac{r}{p}

is equal to

Commented by jagoll last updated on 15/Feb/20

(i) a, b, c i n A P \Rightarrow 2 b = a + c

(i i) a p, b q, c r i n G P \Rightarrow {(b q)}^{2} = a p c r

(i i i) p, q, r i n H P \Rightarrow \frac{1}{q} = \frac{2}{\frac{1}{p} + \frac{1}{r}}

\Rightarrow \frac{1}{p} + \frac{1}{r} = 2 q

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