Let `a_1,a_2,a_3,.....` be in A.P. with common difference not multiple of 3. Then the maximum number of consecutive terms so that all are prime number, is

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

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

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 :

Let a_1,a_2,....a11 are in incresing A.P.and if varience of these number is 90 then value of common difference of A.P. is.

If an A.P a_6 = 2 then common difference for which a_1.a_3.a_6 is least is

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 n arithmetic means between a and b. Then the common difference of the AP is

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