Progression (Sequence and Series)Hard

Question

If x, y, z are in A.P. and tan^-1x, tan^-1y and tan^-1z are also in A.P., then

Options

A.x = y = z

B.2x = 3y = 6z

C.6x = 3y = 2z

D.6x = 4y = 3z

Solution

2y = x + z
and 2tan^-1y = tan^-1x + tan^-1z
⇒
⇒ y² = zx
⇒ x = y = z

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