For three positive integers $p,q,r,x^{pq^{2}} = y^{qr} = z^{p^{2}r}$\n and $r = pq + 1$ such that $3,3\log_{y}x,3\log_{z}y,7\log_{x}z$\n are in A.P...

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For three positive integers p,q,r,x^{pq^{2}} = y^{qr} = z^{p^{2}r} and r = pq + 1 such that 3,3\log_{y}x,3\log_{z}y,7\log_{x}z are in A.P. with common difference 1/2. The r - p - q is equal to: Sequence & Series (Mathematics) Question | DivineJEE

For three positive integers p,q,r,x^{pq^{2}} = y^{qr} = z^{p^{2}r} and r = pq + 1 such that 3,3\log_{y}x,3\log_{z}y,7\log_{x}z are in A.P. with common difference 1/2. The r - p - q is equal to: Sequence & Series (Mathematics) Question | DivineJEE | DivineJEE

Let a,b be two non-zero real numbers. If p and r are the roots of the equation x^{2} - 8ax + 2a = 0 and q and s are the roots of the equation \end{enumerate} x^{2} + 12bx + 6b = 0, such that \frac{1}{p},\frac{1}{q},\frac{1}{r},\frac{1}{s} are in A.P., then a^{- 1} - b^{- 1} is equal to

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