Let `a, b, c` be in A.P. and `|a|lt1,|b|lt1|c|lt1`. If `x=1+a+a^(2)+ . . . ."to "oo,y=1+b+b^(2)+ . . . ."to "ooand,z=1+c+c^(2)+ . . . "to "oo`, then `x, y, z` are in

Options

A. AP
B. GP
C. HP
D. None of these

Answer

C

Explanation

Clearly, `x=(1)/(1-a),y=(1)/(1-b)" and "z=(1)/(1-c)`
Since, a,b,c are in AP.
`implies 1-a,1-b,1-c` ,are also in AP.
`implies (1)/(1-a),(1)/(1-b),(1)/(1-c)` are in HP.
`:. X,y,z` are in HP.