Question

if a,b,c,d are in GP then show that ab,ca,bc,bd are also in GP ?

Answer 1

a÷b=b÷c=c÷d=k
a=bk
b=ck
c=dk
a=(ck)k=ck2
b=(dk)k=dk2
c=dk
now,
ab÷ca=ca÷bc=bc÷bd
then we get,
b÷c=a÷b=c÷d
then we put the values,
dk2÷dk=ck2÷dk2=dk÷d
k÷1=dk÷d=k÷1
k÷1=k÷1=k÷1
so they are also in GP