If `a_1,a_2, .....,a_n` are positive real numbers whose product is a fixed number `c ,` then the minimum value of `a_1+a_2+.........+a_(n-1)+2a_n` is a.`a_(n-1)+2a_n` b. `(n+1)c^(1//n)` c.`2n c^(1//n)` d.`(n)(2c)^(1//n)`

If a-1,a_2, ,a_n are positive real numbers whose product is a fixed number c , then the minimum value of a1 + d2 +..... + an-1 + 2an is

If a_1+a_2+a_3+...+a_n=1AAa_i>0,i=1,2,3, ,n , then find the maximum value of a_1 a_2a_3a_4a_5.... a_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 .

If roots of an equation x^n-1=0 are 1,a_1,a_2,........,a_(n-1) then the value of (1-a_1)(1-a_2)(1-a_3)........(1-a_(n-1)) will be (a) n (b) n^2 (c) n^n (d) 0

Find the first 6 terms of the sequence given by a_1=1, a_n=a_(n-1)+2 , n ge 2

Write the first three terms of the sequence defined by a_1 2,a_(n+1)=(2a_n+3)/(a_n+2) .

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

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)

Find the first five terms of the following sequence . a_1 = 1 , a_2 = 1 , a_n = (a_(n-1))/(a_(n-2) + 3) , n ge 3 , n in N

If a_(1)=-1 and a_(n)=(a_(n-1))/(n+2) then the value of a_(4) is ____.