If in a progression `a_1, a_2, a_3,.......... e tc dot,(a_r-a_(r+1))` bears a constant ratio 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

In an equilateral triangle, inradius r , circumradius R and ex-radius r_1 are in A.P. (b) G.P. (c) H.P. (d) none of these

If the numbers p,q,r are in A.P. then m^(7p), m^(7q), m^(7r)(mgt0) are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If a_n= int_0^pi (sin(2n-1)x)/(sinx) dx . Then the number a_1,a_2,a_3 …….. Are in (A) A.P (B) G.P (C) H.P (D) none of these

If a_1,a_2,a_3,. . . ,a_n. . . are in A.P. such that a_4−a_7+a_10=m , then sum of the first 13 terms of the A.P.is

Let a_1,a_2,a_3…………., a_n be positive numbers in G.P. For each n let A_n, G_n, H_n be respectively the arithmetic mean geometric mean and harmonic mean of a_1,a_2,……..,a_n On the basis of above information answer the following question: A_k,G_k,H_k are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If a,b,c are in A.P ,then 3^(a),3^(b),3^(c) shall be in (A) A.P (B) G.P (C) H.P (D) None of these

Let a_1,a_2,a_3 ......, a_n are in A.P. such that a_n = 100 , a_40-a_39=3/5 then 15^(th) term of A.P. from end is

If a_1,a_2,a_3……..a_n are in H.P. and f(k) = sum_(r=1)^na_r-a_k then (f(1))/a_1, (f(2))/a_3 ….f(n)/a_n are (A) A.P. (B) G.P. (C) H.P. (D) none of these

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

"If "a_1,a_2,a_3,.....,a_n" are in AP, prove that "a_(1)+a_(n)=a_(r)+a_(n-r+1)""