Question

If $x,1,z$ are in AP and $x,2,z$ are in GP, then $x,4;z$ will be in

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

Answer 1

Answer: (C)

HP

Since $x,1$ and $z$ are in AP
Then, $2=x+z$ ...(i)
and $x,2,z$ are in GP
$\therefore 4=xz$ ...(ii)
On dividing Eq (ii) by Eq (i), we get
$\frac{x.z}{x+z}=\frac{4}{2}$

$\Rightarrow \frac{2xz}{x+z}=4$
Hence, $x,4$ and $z$ will be HP.