Let,`a_1,a_2_a,a_3,….` be in harmonic progression with `a_1=5 " and " a_(20)=25` The least positive integer n for which `a_n lt 0 `

Let a_1,a_2,a_3,... be in harmonic progression with a_1=5a n da_(20)=25. The least positive integer n for which a_n<0

Let a_(1),a_(2),a_(3), . . . be a harmonic progression with a_(1)=5anda_(20)=25 . The least positive integer n for which a_(n)lt0 , is

Let a_(1), a_(2), a_(3),..., a_(100) be an arithmetic progression with a_(1) = 3 and S_(p) = sum_(i=1)^(p) a_(i), 1 le p le 100 . For any integer n with 1 le n le 20 , let m = 5n . If (S_(m))/(S_(n)) does not depend on n, then a_(2) is equal to ....

Let a_1,a_2,a_3 ….and b_1 , b_2 , b_3 … be two geometric progressions with a_1= 2 sqrt(3) and b_1= 52/9 sqrt(3) If 3a_99b_99=104 then find the value of a_1 b_1+ a_2 b_2+…+a_nb_n

Consider a sequence {a_n} with a_1=2 & a_n =(a_(n-1)^2)/(a_(n-2)) for all n ge 3 terms of the sequence being distinct .Given that a_2 " and " a_5 are positive integers and a_5 le 162 , then the possible values (s) of a_5 can be

If a_(1), a_(2) …… a_(n) = n a_(n - 1) , for all positive integer n gt= 2 , then a_(5) is equal to

If a_1,a_2,a_3 ,….""a_n is an aritmetic progression with common difference d. prove that tan [ tan ^(-1) ((d)/( 1+ a_1a_2))+ tan^(-1) ((d)/(1+a_2a_3))+…+((d)/(1+a_n a_( n-1))) ] = (a_n -a_1)/(1 +a_1 a_n )

Let a_1, a_2, a_3, ,a_(101) are in G.P. with a_(101)=25a n dsum_(i=1)^(201)a_1=625. Then the value of sum_(i=1)^(201)1/(a_1) equals____________.

Let a_(1), a_(2) ...be positive real numbers in geometric progression. For n, if A_(n), G_(n), H_(n) are respectively the arithmetic mean, geometric mean and harmonic mean of a_(1), a_(2),..., a_(n) . Then, 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 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 .