Let `a_1,a_2,a_3…………., a_n` be positive numes in G.P. For each n let `A_n, G_n, H_n` be respectively the arithmetic mean geometic mean dn harmonic mean of `a_1,a_2,……..,a_n` On the basis of abvoe informtion answer the following question: `A_k,G_k,H_k` are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

Let a_1,a_2,a_3…………., a_n be positive numbers in G.P. For each n let A_n, G_n, H_n be respectively the arithmetic mean geometric mean and harmonic mean of a_1,a_2,……..,a_n On the basis of above information answer the following question: A_k,G_k,H_k are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

.Let a_1, a_2,............ be positive real numbers in geometric progression. For each n, let A_n G_n, H_n , be respectively the arithmetic mean, geometric mean & harmonic mean of a_1,a_2..........a_n . Find an expression ,for the geometric mean of G_1,G_2,........G_n in terms of A_1, A_2,........ ,A_n, H_1, H_2,........,H_n .

Let an A.P. a G.P. and a H.P. of positive terms have the same first term a, the same last term b and the same numberof terms (2n+1). Let x,y,z be the (n+1)th terms respectively of the A.P., G.P. and H.P. respectively. On the basis of above information anwer the following question: x,y,z are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If a,b,c,d are distinct positive then a^n/b^ngtc^n/d^n for all epsilon N if a,b,c,d are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If a_n= int_0^pi (sin(2n-1)x)/(sinx) dx . Then the number a_1,a_2,a_3 …….. Are in (A) A.P (B) G.P (C) H.P (D) none of these

If a_n= int_0^pi (sin(2n-1)x)/(sinx) dx . Then the number a_1,a_2,a_3 …….. Are in (A) A.P (B) G.P (C) H.P (D) none of these

If x,a_1,a_2,a_3,…..a_n epsilon R and (x-a_1+a_2)^2+(x-a_2+a_3)^2+…….+(x-a_(n-1)+a_n)^2le0 , then a_1,a_2,a_3………a_n are in (A) AP (B) GP (C) HP (D) none of these

Write the first five terms in each of the following sequence: a_1=a_2=2,\ a_n=a_(n-1)-1,\ n >1 .

Arithmetic mean a, geometric mean G and Harmonic mean H to n positive numbers a_1,a_2,a_3,…..,a_n are given by A=(a_1+a_2+……………+a_n)/n, G=(a_1 a_2 a_n)^(1/2) and G= n/(1/H_1+1/H_2+………+1/H_n) There is a relation in A, G and H given by AgeGgeH equality holds if and only if a_1=a_2=..............=a_n On the basis of above information answer the following question If a_rgt0 or r=1,2,.......6 and a_1+a_2+.....+a_6=3, M=(a_1+a_2)(a_3+a_4)(a_5+a_6) . Then the set of all possible values of M is (A) (0,3] (B) (0,2] (C) (0,1] (D) none of these

rithmetic mean a, geometric mean G and Harmonic mean H to n positive numbers a_1,a_2,a_3,…..,a_n are given by A=(a_1+a_2+……………+a_n)/n, G=(a_1 a_2 a_n)^(1/2) and G= n/(1/H_1+1/H_2+………+1/H_n) There is a relation in A, G and H given by AgeGgeH equality holds if and only if a_1=a_2=..............=a_n On the basis of above information answer the following question If a,b,c are positive numers such that a+b+c=0 then greatest value a^3b^2c^5 is (A) 3^3.2^2.5^5 (B) 3^10 (C) 2^10 (D) 5^10