For an increasing A.P. `a_1, a_2,..... a_n ifa_1+a_3+a_5=-12` and `a_1a_3a_5=80 ,` then which of the following is/are true? a.`a_1=-10` b. `a_2=-1` c. `a_3=-4` d. `a_5=+2`

Consider an A. P .a_1,a_2,a_3,..... such that a_3+a_5+a_8 =11and a_4+a_2=-2 then the value of a_1+a_6+a_7 is.....

Let a_1,a_2,a_3…… ,a_n be in G.P such that 3a_1+7a_2 +3a_3-4a_5=0 Then common ratio of G.P can be

If in a progression a_1, a_2, a_3, e t cdot,(a_r-a_(r+1)) bears a constant atio with a_rxxa_(r+1) , then the terms of the progression are in a. A.P b. G.P. c. H.P. d. none of these

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.

If a_(n+1)=1/(1-a_n) for n>=1 and a_3=a_1 . then find the value of (a_2001)^2001 .

Let a_1, a_2, ,a_(10) be in A.P. and h_1, h_2, h_(10) be in H.P. If a_1=h_1=2a n da_(10)=h_(10)=3,t h e na_4h_7 is

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

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

In a four-dimensional space where unit vectors along the axes are hat i , hat j , hat ka n d hat l ,a n d vec a_1, vec a_2, vec a_3, vec a_4 are four non-zero vectors such that no vector can be expressed as a linear combination of others and (lambda-1)( vec a_1- vec a_2)+mu( vec a_2+ vec a_3)+gamma( vec a_3+ vec a_4-2 vec a_2)+ vec a_3+delta vec a_4=0, then a. lambda=1 b. mu=-2//3 c. gamma=2//3 d. delta=1//3

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____________.