If `a_1, a_2, a_3,54,a_6,a_7, a_8, a_9` are in H.P., and `D=|[a_1,a_2,a_3],[5, 4,a_6],[a_7,a_8,a_9]|` , then the value of `[D]i sw h e r e[dot]` represents the greatest integer function

If a_1, a_2, a_3,54,a_6,a_7, a_8, a_9 are in H.P., and D=|a_1a_2a_3 5 4a_6a_7a_8a_9| , then the value of [D]i sw h e r e[dot] represents the greatest integer function

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_r=(cos2rpi+i sin 2rpi)^(1//9) , then prove that |[a_1,a_2,a_3],[a_4,a_5,a_6],[a_7,a_8,a_9]|=0 .

a_1,a_2, a_3, ,a_n are in A.P. and a_1+a_3+a_5+a_7+a_9=20 then a_5 is 2 2. 7 3. 3 4. 4 5. 5

Suppose a_1, a_, are real numbers, with a_1!=0. If a_1, a_2,a_3, are in A.P., then (a) A=[(a_1,a_2,a_3),(a_4,a_5,a_6),(a_5,a_6,a_7)] is singular (where i=sqrt(-1)) (b)The system of equations a_1x+a_2y+a_3z=0,a_4x+a_5y+a_6z=0,a_7x+a_8y+a_9=0 has infinite number of solutions. (c) B=[(a_1,i a_2),(ia_2,a_1)] is non-singular (d)none of these

If for an A.P. a_1,a_2,a_3,........,a_n,........a_1+a_3+a_5=-12 and a_1a_2a_3=8, then the value of a_2+a_4+a_6 equals

Let a_1, a_2, a_3, ....a_n,......... be in A.P. If a_3 + a_7 + a_11 + a_15 = 72, then the sum of itsfirst 17 terms is equal to :

If a_1,a_2,a_3,a_4 are in HP , then 1/(a_1a_4)sum_(r=1)^3a_r a_(r+1) is root of :

If a_1, a_2, ,a_n are in H.P., then (a_1)/(a_2+a_3++a_n),(a_2)/(a_1+a_3++a_n), ,(a_n)/(a_1+a_2++a_(n-1)) are in a. A.P b. G.P. c. H.P. d. none of these

Three distinct numbers a_1 , a_2, a_3 are in increasing G.P. a_1^2 + a_2^2 + a_3^2 = 364 and a_1 + a_2 + a_3 = 26 then the value of a_10 if a_n is the n^(th) term of the given G.P. is: A. 2.3^9 B. 3^9 C. 2.3^(10) D. 3^(12)