If a,b,c be in GP and p,q be respectively AM between a,b and b,c then

(a) 2/b=1/p+1/q
(b) 2/b=1/p-1/q
(c) 2=a/p-c/q
(d) None of the above

• Option (a)
  
  p=(a+b)/2; q=(b+c)/2
  
  1/p+1/q = 2*((1/(a+b))+(1/(b+c))
  = 2*(a+2b+c)/(a+b)(b+c)
  = 2*(a+2ar+a(r^2))/(a+ar)(ar+a(r^2)) because b=ar; c= a(r^2)
  
  where r - common ratio
  
  On simplication
  
  1/p+1/q = 2/ar = 2/b
  
• 12 years agoHelpfull: Yes(9) No(3)
• Ans:d
  Assume a,b,c=2,4,8
  p,q=2,4 then none of a or b or c satisfied.
• 12 years agoHelpfull: Yes(2) No(2)