If p- q- r are in A-P- and a-x-p x-a-y-q y-a-z-r z- then x- y- z are in

The correct option is C H.PLet a x/px = a y/qy = a z/rz = k, say p = a x/kx, q = a y/ky,r = a z/kz are in A.P. (given) a x/px = a y/qy = a z/rz are in A.P. ...

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Standard XII

Mathematics

nth Term of A.P

If p, q, r ar...

Question

If p, q, r are in A.P. and $\frac{a - x}{p x} = \frac{a - y}{q y} = \frac{a - z}{r z}$ , then x,y,z are in

A.P

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G.P

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H.P

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none of these

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Solution

The correct option is C H.P
$L e t \frac{a - x}{p x} = \frac{a - y}{q y} = \frac{a - z}{r z} = k, s a y p = \frac{a - x}{k x}, q = \frac{a - y}{k y}, r = \frac{a - z}{k z} a r e i n A . P . (g i v e n)$
$\frac{a - x}{p x} = \frac{a - y}{q y} = \frac{a - z}{r z} a r e i n A . P . \frac{a}{x} - 1, \frac{a}{y} - 1, \frac{a}{z} - 1 a r e i n A . P .$
$\Rightarrow \frac{a}{x}, \frac{a}{y}, \frac{a}{z} a r e i n A . P . \Rightarrow \frac{1}{x}, \frac{1}{y}, \frac{1}{z} a r e i n A . P . \Rightarrow x, y, z$ are in H.P.

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If p, q, r are in A.P. and a−xpx=a−yqy=a−zrz, then x,y,z are in

The correct option is C H.PLeta−xpx=a−yqy=a−zrz=k,sayp=a−xkx,q=a−yky,r=a−zkz are in A.P. (given) a−xpx=a−yqy=a−zrzare in A.P.ax−1,ay−1,az−1 are in A.P. ⇒ax,ay,az are in A.P.⇒1x,1y,1z are in A.P.⇒x,y,z are in H.P.

If p, q, r are in A.P. and $\frac{a - x}{p x} = \frac{a - y}{q y} = \frac{a - z}{r z}$ , then x,y,z are in