Question

(D) 6454
If x, y, z are in AP, a is AM between x and y
and b is AM tetween y and z, then AM
between a and b will be-
(A) = (x + y +z)
(B) z
(C) x
D) y​

Answer 1

Answer:

$\textbf{A.M of a and b is y}$

option (d) is correct

Step-by-step explanation:

$\text{Concept used:}$

$\textbf{If a,b,c are in A.P, b=\frac{a+c}{2} }$

since x, y, z are in A.P, $y=\frac{x+z}{2}$

$\implies\:2y=x+z$........(1)

since a is the A.M of x and y, we have

$a=\frac{x+y}{2}$

since b is the A.M of y and z, we have

$b=\frac{y+z}{2}$

Now,

A.M of a and b

$=\frac{\frac{x+y}{2}+\frac{y+z}{2}}{2}$

$=\frac{\frac{x+2y+z}{2}}{2}$

$=\frac{x+2y+z}{4}$

$=\frac{2y+2y}{4}$            (using (1))

$=\frac{4y}{4}$

$=y$

$\implies\:\boxed{\textbf{A.M of a and b is y}}$