99 Percentile Qs Bank for JEE MainMathematicsSequences and Series
If x, y, z are in A.P. and ⁻¹ x, ⁻¹ y and ⁻¹ z are also in A.P., then
Options
- Ax=y= z
- B2 x=3 y=6 z
- C6 x=3 y=2 z
- D6 x=4 y=3 z
Correct answer
A. x=y= z
Step-by-step solution
Given, x, y, z are in A.P. 2 y=x+z... (i) Also, aligned & ⁻¹ x, ⁻¹ y, ⁻¹ z are in A.P. & 2 ⁻¹ y= ⁻¹ x+ ⁻¹ z & ⁻¹ ( 2 y 1-y^2 )= ⁻¹ ( x+z 1-x z ) & 2 y 1-y^2 = x+z 1-x z & 2 y 1-y^2 = 2 y 1-x z ... [From (i)] & 1-y^2=1-x z & y^2=x z aligned x, y, z are in G.P. ... (ii) From (i) and (ii), we get x=y= z