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.`

For the A.P., a_1, a_2,a_3, ............., if a_4/a_7= 2/3 , find a_6/a_8 .

If for an A.P. a_1,a_2,a_3,........,a_n,........a_1+a_3+a_5=-12 and a_1a_2a_3=8, then the value of a_2+a_4+a_6 equals

Let A_1 , A_2 …..,A_3 be n arithmetic means between a and b. Then the common difference of the AP is

Find the sum first 24 terms of A.P. a_1,a_2,a_3 ,..........., if it is know that a_1+a_5+a_10+a_15+a_20+a_24=225

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

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,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 :

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

The terms a_1, a_2, a_3 from an arithmetic sequence whose sum s 18. The terms a_1+1,a_2, a_3,+2, in that order, form a geometric sequence. Then the absolute value of the sum of all possible common difference of the A.P. is ________.

The terms a_1, a_2, a_3 from an arithmetic sequence whose sum s 18. The terms a_1+1,a_2, a_3,+2, in that order, form a geometric sequence. Then the absolute value of the sum of all possible common difference of the A.P. is ________.