Question

If a,b,c,d are in g.p then prove that a+b,b+c,c+d are also in g.p

Answer 1

Answer:

As proven in steps

Step-by-step explanation:

consider (a+b)*(c+d)

=a*c+a*d+b*c+b*d

=b^2+a*d+b*c+c^2 since ac=b^2 and bd=c^2 from given GP

=b^2+b*c+b*c+c^2 since b/a=d/c i e. bc =ad from given GP

=b^2+c^2+2bc=(b+c)^2

hence (a+b) ,(b+c) and (c+d) are in GP