If `f(x+y)=f(x).f(y)` and `a1,a2,a3` are in A.P, then `f(a1),f(a2),f(a3)` are in
A. AP
B. GP
C. HP
D. None

If x,a_1,a_2,a_3,…..a_n epsilon R and (x-a_1+a_2)^2+(x-a_2+a_3)^2+…….+(x-a_(n-1)+a_n)^2le0 , then a_1,a_2,a_3………a_n are in (A) AP (B) GP (C) HP (D) none of these

Let a_1,a_2 ,a_3 …..be in A.P. and a_p, a_q , a_r be in G.P. Then a_q : a_p is equal to :

If a_1,a_2, a_3………. are in H.P. and f(k) =sum_(r=1)^n a_r-a_k, the a_1/(f(1)), a_2/(f(2)), a_3/(f(3)), …….., a_n/(f(n)) 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

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

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