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 find common ratio of G.P.

Let a_1, a_2, a_3, ?a_10 are in G.P. if a_3/a_1 =25 then a_9/a_5 is equal to (A) 5^4 (B) 4.5^4 (C) 4.5^3 (D) 5^3

Consider an A.P. a_1, a_2, a_3,......... such that a_3+a_5+a_8=11 and a_4+a_2=-2, then the value of a_1+a_6+a_7 is (a). -8 (b). 5 (c). 7 (d). 9

Let A_r ,r=1,2,3, , be the points on the number line such that O A_1,O A_2,O A_3dot are in G P , where O is the origin, and the common ratio of the G P be a positive proper fraction. Let M , be the middle point of the line segment A_r A_(r+1.) Then the value of sum_(r=1)^ooO M_r is equal to (a) (O A_1(O S A_1-O A_2))/(2(O A_1+O A_2)) (b) (O A_1(O A_2+O A_1))/(2(O A_1-O A_2) (c) (O A_1)/(2(O A_1-O A_2)) (d) oo

If x ,2y ,3z are in A.P., where the distinct numbers x ,y ,z are in G.P, then the common ratio of the G.P. is a. 3 b. 1/3 c. 2 d. 1/2

If the average of ( a_1, a_2 , a_3………………. , a_n) be bar a then the average ( xa_1 , xa_2, xa_3,……………….. xa_n) , where x ne 0 ,will be …………….

If a_1,a_2,a3,...,a_n are in A.P then show that 1/(a_1a_2)+1/(a_2a_3)+1/(a_3a_4)+...+1/(a_(n-1)a_n)=(n-1)/(a_1a_n)

If a_1,a_2,.....a_n are in H.P., then the expression a_1a_2 + a_2a_3 + ... + a_(n-1)a_n is equal to

The number of all possible triplets (a_1,a_2,a_3) such that : a_1 + a_2cos2x + a_3sin^2x = 0 for all x is :

If a ,a_1, a_2, a_3, a_(2n),b are in A.P. and a ,g_1,g_2,g_3, ,g_(2n),b . are in G.P. and h s the H.M. of aa n db , then prove that (a_1+a_(2n))/(g_1g_(2n))+(a_2+a_(2n-1))/(g_1g_(2n-1))++(a_n+a_(n+1))/(g_ng_(n+1))=(2n)/h

If a_0, a_1, a_2, a_3 are all the positive, then 4a_0x^3+3a_1x^2+2a_2x+a_3=0 has least one root in (-1,0) if (a) a_0+a_2=a_1+a_3 and 4a_0+2a_2>3a_1+a_3 (b) 4a_0+2a_2<3a_1+a_3 (c) 4a_0+2a_2=3a_1+a_0 and 4a_0+a_2lta_1+a_3 (d) none of these