Question

if p,q,r are in gp and p^1/x = q^ 1/y = r^1/z ,verify whether x,y,z are in AP GP or neither​

Answer 1

Answer:

p,q,r are in AP

Let the common difference be d

⟹d=q−p=r−q

2d=r−p

x,y,z are in GP

Condition to be in GP

y

2

=xz

y

2d

=x

d

z

d

x

−(r−q)

z

−(q−p)

y

r−p

=1

x

q−r

.y

r−p

.z

p−q

=1

Answer By Shaurya

Answer 2

Answer:

p,q,r are in AP

Let the common difference be d

⟹d=q−p=r−q

2d=r−p

x,y,z are in GP

Condition to be in GP

y

2

=xz

y

2d

=x

d

z

d

x

−(r−q)

z

−(q−p)

y

r−p

=1

x

q−r

.y

r−p

.z

p−q

=1