If `a_1, a_2, a_3(a_1>0)` are three successive terms of a G.P. with common ratio `r ,` for which `a+3>4a_2-3a_1` holds is given by a. `1ltrltrarr3` b. `-3ltrlt-1` c. `r gt3 or rlt1` d. none of these

if b_(1),b_(2),b_(3)(b_(1)gt0) are three successive terms of a G.P. with common ratio r , the value of for which the inequality b_(3)gt4b_(2)-3b_(1) , holds is given by

If a_1, a_2, a_3,...a_20 are A.M's inserted between 13 and 67 then the maximum value of the product a_1 a_2 a_3...a_20 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 1, a_1,a_2,a_3 ,…, a_(n-1) are the nth roots of unity then prove that : (1-a_1)(1-a_2)(1-a_3)...(1-a_(n-1)) =n.

If 1, a_1,a_2,a_3 ,…, a_(n-1) are the nth roots of unity then prove that : 1+a_1+a_2+…+a_(n-1) =0.

The average of a_1, a_2, a_3, a_4 is 16. Half of the sum of a_2, a_3, a_4 is 23. What is the value of a_1

We know that, if a_1, a_2, ..., a_n are in H.P. then 1/a_1,1/a_2,.....,1/a_n are in A.P. and vice versa. If a_1, a_2, ..., a_n are in A.P. with common difference d, then for any b (>0), the numbers b^(a_1),b^(a_2),b^9a_3),........,b^(a_n) are in G.P. with common ratio b^d. If a_1, a_2, ..., a_n are positive and in G.P. with common ration, then for any base b (b> 0), log_b a_1 , log_b a_2,...., log_b a_n are in A.P. with common difference logor.If x, y, z are respectively the pth, qth and the rth terms of an A.P., as well as of a G.P., then x^(z-x),z^(x-y) is equal to

a_1, a_2, a_3 …..a_9 are in GP where a_1 lt 0, a_1 + a_2 = 4, a_3 + a_4 = 16 , if sum_(i=1)^9 a_i = 4 lambda then lambda is equal to

If a_1, a_2, a_3,...a_n are in A.P with common difference d !=0 then the value of sind(coseca_1 coseca_2 +cosec a_2 cosec a_3+...+cosec a_(n-1) cosec a_n) will be

If a_1,a_2,a_3 are in G.P. having common ratio r such that sum_(k=1)^n a_(2k-1)= sum_(k=1)^na_(2k+2)!=0 then number of possible value of r is (A) 1 (B) 2 (C) 3 (D) none of these