Class 11

Math

Algebra

Sequences and Series

If $a_{1/x}=b_{1/y}=c_{1/z}anda,b,cinG.p.,Thenx,y,zarein$

- A.P
- G.P
- H.P
- None

Let

$a_{1/x}=b_{1/y}=c_{1/z}=k$

So,

$a=k_{x},b=k_{y},c=k_{z}$

Since,

$a,b,c$ are in $G.P$

So,

$b_{2}=ac$

Now,

$k_{2y}=k_{x}.k_{z}$

$k_{2y}=k_{x+z}$

Therefore,

$2y=x+z$

Hence, $x,y,z$ are in $A.P$