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`

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

Let a_1,a_2,a_3 …. a_n be in A.P. If 1/(a_1a_n)+1/(a_2a_(n-1)) +… + 1/(a_n a_1) = k/(a_1 + a_n) (1/a_1 + 1/a_2 + …. 1/a_n) , then k is equal to :

If a_1,a_2,a_3,……a_n are in A.P. [1/(a_1a_n)+1/(a_2a_(n-1))+1/(a_3a_(n-2))+..+1/(a_na_1)]

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

A sequence of positive integers a_1 , a_2, a_3, …..a_n is given by the rule a_(n + 1) = 2a_(n) + 1 . The only even number in the sequence is 38. What is the value of a_2 ?

Let a_1, a_2, a_3, ...a_(n) be an AP. then: 1 / (a_1 a_n) + 1 / (a_2 a_(n-1)) + 1 /(a_3a_(n-2))+......+ 1 /(a_(n) a_1) =

If a_1, a_2, a_3,.....a_n are in H.P. and a_1 a_2+a_2 a_3+a_3 a_4+.......a_(n-1) a_n=ka_1 a_n , then k is equal to

If a_0, a_1 , a_2 …..a_n are binomial coefficients then (1 + a_1/a_0)(1 +a_2/a_1) …………….(1 + (a_n)/(a_(n-1)) ) =

If a_1,a_2,a_3, ,a_n are an A.P. of non-zero terms, prove that 1/(a_1a_2)+1/(a_2a_3)++1/(a_(n-1)a_n)= (n-1)/(a_1a_n)

A sequence of number a_1, a_2, a_3,…..,a_n is generated by the rule a_(n+1) = 2a_(n) . If a_(7) - a_(6) = 96 , then what is the value of a_(7) ?