Question

if a,b,c,d are in gp , show that a+b,b+c,c+d are in gp

Answer 1

let
a=a
b=ar
c=ar^2
d=ar^3
a+b=a (1+r)
b+c=ar (1+r)
c+dar^2 (1+r)
which is also in go with common ratio r and first term with a(1+r)