Q. If $x,\ 1,\ \mathcal{z}$ are in AP and $x,\ 2,\ \mathcal{z}$ are in GP, then $x,\ 4,\ \mathcal{z}$ will be in
A) AP
B) GP
C) HP
D) None of these
Explanation
(c)
$x,1,\ \mathcal{z}$ are in AP, then $2 = x + \mathcal{z}$ …(i)
And $x,\ 2,\ \mathcal{z}$ are in GP, then $4 = x\mathcal{z}$ …(ii)
Divide Eq.(ii) by Eq.(i), we get
$\frac{x\mathcal{z}}{x + \mathcal{z}} = \frac{4}{2}\ \Rightarrow \ \frac{2x\mathcal{z}}{x + \mathcal{z}}$=4
Hence, $x,\ 4,\ \mathcal{z}$ will be in HP.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.