if pth ,qth and rth terms of a G P are themselves in G P ,show that p,q,r are - Maths - Sequences and Series

Question

if pth ,qth and rth terms of a
G P are themselves in G P ,show that p,q,r are in A P

Ajinder Singh · Answer

AP= arp-1 , Aq =
arq-1,Ar = arr-1
now arp-1 , arq-1 , arr-1
are in gp
that means arq-1 / arp-1 =
arr-1 / arq-1
r q-1 / rp-1 = rr-1 /
rq-1
r q-1-p+1 = rr-1-q+!
rq-p = rr-q
i e q-p = r-q
2q = p+r
therefore p,q,r are in AP

if pth ,qth and rth terms of a G.P. are themselves in G.P.,show that p,q,r are in A.P.

if p^th ,q^th and r^th terms of a G.P. are themselves in G.P.,show that p,q,r are in A.P.