If distinct positive number `b_1,b_2 and b_3` are in G.P. then `f(1)+In b_1,f(2)+In b_2,f(3)+ In b_3` are in :

Let f (x) be a continuous function (define for all x) which satisfies f ^(3) (x)-5 f ^(2) (x)+ 10f (x) -12 ge 0, f ^(2) (x) + 3 ge 0 and f ^(2) (x) -5f(x)+ 6 le 0 If distinct positive number b_(1), b _(2) and b _(3) ar in G.P. then f (1)+ ln b _1), f (2) + ln b _(2), f (3)+ ln b _(3) are in :

Let f (x) be a continuous function (define for all x) which satisfies f ^(3) (x)-5 f ^(2) (x)+ 10f (x) -12 ge 0, f ^(2) (x) + 3 ge 0 and f ^(2) (x) -5f(x)+ 6 le 0 If distinct positive number b_(1), b _(2) and b _(3) ar in G.P. then f (1)+ ln b _91), f (2) + ln b _(2), f (3)+ ln b _(3) are in :

Suppose four distinct positive numbers a_1,a_2,a_3,a_4 are in G.P. Let b_1=a_1,b_2=b_1+a_2,b_3=b_2+a_3 and b_4=b_3+a_4 . Statement -1 : The numbers b_1,b_2,b_4 are neither in A.P. nor in G.P. and Statement -2 : The numbers b_1,b_2,b_3,b_4 are in H.P.

Suppose four distinct positive numbers a_(1),a_(2),a_(3),a_(4) are in G.P. Let b_(1)=a_(1),b_(2)=b_(1)+a_(2),b_(3)=b_(2)+a_(3)andb_(4)=b_(3)+a_(4) . Statement -1 : The numbers b_(1),b_(2),b_(3),b_(4) are neither in A.P. nor in G.P. Statement -2: The numbers b_(1),b_(2),b_(3),b_(4) are in H.P.

Suppose four distinct positive numbers a_1, a_2, a_3, a_4, are in G.P. Let b_1=a_1,b_2=b_1+a_2.b_3=b_2+a_3 and b_4=b_3+a_1.

Suppose four distinct positive numbers a_(1),a_(2),a_(3),a_(4) are in G.P. Let b_(1)=a_(1), b_(2)=b_(1)+a_(2),b_(3)=b_(2)+a_(3)andb_(4)=b_(3)+a_(4) . Statement -1 : The numbers b_(1),b_(2),b_(3),b_(4) are neither in A.P. nor in G.P. Statement -2: The numbers b_(1),b_(2),b_(3),b_(4) are in H.P.

Suppose four distinct positive numbers a_(1),a_(2),a_(3),a_(4) are in G.P.Let b_(1)=a_(1),b_(2)=b_(1)+a_(2)*b_(3)=b_(2)+a_(3) and b_(4)=b_(3)+a_(1)

Suppose four distinct positive numbers a_(1),a_(2),a_(3),a_(4) are in G.P. Let b_(1)=a_(1)+,a_(b)=b_(1)+a_(2),b_(3)=b_(2)+a_(3)andb_(4)=b_(3)+a_(4) . Statement -1 : The numbers b_(1),b_(2),b_(3),b_(4) are neither in A.P. nor in G.P. Statement -2: The numbers b_(1),b_(2),b_(3),b_(4) are in H.P.