Question

If $x,y,z$ are in A.P. and A.M. of $x$ and $y$ is a and that to $y$ and $z$ is $b$, then A.M. of $a$ and $b$ is.

• A. $x$
• B. $y$
• C. $z$
• D. $\frac{1}{2(x+y)}$

Answer 1

The correct option is B $y$

Given $x,y,z$ are in A.P $\Rightarrow 2y=x+z$
${}^{\prime }{a}^{\prime }$ is A.M of ${}^{\prime }{x}^{\prime }$ and ${}^{\prime }{y}^{\prime }$ $\Rightarrow a=\frac{x+y}{2}$
and ${}^{\prime }{b}^{\prime }$ is A.M of ${}^{\prime }{y}^{\prime }$ and ${}^{\prime }{z}^{\prime }$ $\Rightarrow b=\frac{y+z}{2}$
$\therefore$ A.M of $a$ and $b$ is $=\frac{a+b}{2}=\frac{x+2y+z}{4}=y$
Hence, option 'B' is correct.