For the A.P. given by `a_1,a_2,.....,a_n,....,` with non-zero common difference, the equations satisfied are-

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_n are in A.P.with common difference d ne 0 , then [sin d] [sec a_1 sec a_2 + sec a_2sec a_3+............+ sec a_(n-1) sec a_n] is equal to :

If a_1, a_2,a_3,..........., a_n are in A.P. with common difference d, prove that : sin d [cosec a_1 coseca_2+ coseca_2coseca_3+....coseca_(n-1)coseca_n]= cot a_1-a_n .

Let a_1,a_2,a_3,... be in A.P. With a_6=2. Then the common difference of the A.P. Which maximises the product a_1a_4a_5 is :

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,...,a_n be in AP whose common difference is d then prove that sum_(i=1)^n a_ia_(i+1)=n{a_1^2+na_1d+(n^2-1)/3 d^2} .

The sixth term of an A.P., a_1,a_2,a_3,.............,a_n is 2 . If the quantity a_1a_4a_5 , is minimum then then the common difference of the A.P.

let a_1,a_2,...a_n be in A.P. wth common difference pi/6 . if seca_1seca_2+seca_2seca_3+....seca_(n-1)seca_n = k(tana_n-tana_1) Find the value of k