Question

If p,q,r,s are in G.P. show that p+q, q+r, r+s are in G.P.​

Answer 1

Answer:

Step-by-step explanation:

SO p=a

   q=ar

  r=ar²

 s=ar³

p+q=a+ar=a(1+r)

q+r=ar+ar²=ar(1+r)    

r+s=ar²+ar³=ar²(1+r)

r+s/q+r=r=q+r/p+q

∴ p+q, q+r, r+s are in GP

Answer 2

Answer:

Proof below. Hope it helps! <3

Step-by-step explanation:

Let common ratio be d.

Then, q=pd, r=pd² and s=pd³

p+q=p+pd=p(1+d)

q+r=pd+pd²=pd(1+d)=p(1+d)*d=(p+q)*d

r+s=pd²+pd³=pd²(1+d)=p(1+d)*d²=(p+q)*d*d=(q+r)*d

Common ratio among p+q, q+r and r+s is d.

Thus, p+q, q+r and r+s also form GP.