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 ________.

If a_1, a_2, a_3(a_1>0) are three successive terms of a G.P. with common ratio r , for which a_3>4a_2-3a_1 holds is given by

Find the number of all three elements subsets of the set {a_1, a_2, a_3, a_n} which contain a_3dot

If the arithmetic progression whose common difference is nonzero the sum of first 3n terms is equal to the sum of next n terms. Then, find the ratio of the sum of the 2n terms to the sum of next 2n terms.

If a-1,a_2, ,a_n are positive real numbers whose product is a fixed number c , then the minimum value of a1 + d2 +..... + an-1 + 2an is

Which of the following sequence are Arithmetice progression ? If it is an A.P. then write common difference. -1, (-3)/(2) , -2, -5/2 , ……

A vector a has components a_1,a_2,a_3 in a right handed rectangular cartesian coordinate system OXYZ the coordinate axis is rotated about z axis through an angle pi/2 . The components of a in the new system

Find the first 6 terms of the sequence given by a_1=1, a_n=a_(n-1)+2 , n ge 2

Let a_1,a_2,a_3,... be in harmonic progression with a_1=5a n da_(20)=25. The least positive integer n for which a_n<0

In a four-dimensional space where unit vectors along the axes are hat i , hat j , hat ka n d hat l ,a n d vec a_1, vec a_2, vec a_3, vec a_4 are four non-zero vectors such that no vector can be expressed as a linear combination of others and (lambda-1)( vec a_1- vec a_2)+mu( vec a_2+ vec a_3)+gamma( vec a_3+ vec a_4-2 vec a_2)+ vec a_3+delta vec a_4=0, then a. lambda=1 b. mu=-2//3 c. gamma=2//3 d. delta=1//3