Does there exist a geometric progression containing 27, 8 and 12 as three of its terms. If it exists, how many such progressions are possible ?

The first term of a geometric progression whose second term is 2 and sum to infinity is 8 will be

The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

In a geometric progression with first term a and common ratio r, what is the arithmetic mean of first five terms ?

Verify that 10,-9, 8.1,..... is a geometric progression. Find the sum to infinity of the G.P.

Three boys and three girls are to be seated around a table in a circle. Among them, the boy X does not want any girl neighbour and the girl Y does not want any boy neighbour. How many such arrangements are possible ?

Let A be nxxn matrix given by A=[(a_(11),a_(12),a_(13)……a_(1n)),(a_(21),a_(22),a_(23)…a_(2n)),(vdots, vdots, vdots),(a_(n1),a_(n2),a_(n3).a_("nn"))] Such that each horizontal row is arithmetic progression and each vertical column is a geometrical progression. It is known that each column in geometric progression have the same common ratio. Given that a_(24)=1,a_(42)=1/8 and a_(43)=3/16 Let d_(i) be the common difference of the elements in with row then sum_(i=1)^(n)d_(i) is

Let A be nxxn matrix given by A=[(a_(11),a_(12),a_(13)……a_(1n)),(a_(21),a_(22),a_(23)…a_(2n)),(vdots, vdots, vdots),(a_(n1),a_(n2),a_(n3).a_("nn"))] Such that each horizontal row is arithmetic progression and each vertical column is a geometrical progression. It is known that each column in geometric progression have the same common ratio. Given that a_(24)=1,a_(42)=1/8 and a_(43)=3/16 .Let Di be the common difference of i^(th) row The value of lim_(nto oo)sum_(i=1)^(n)D_(i) is equal to

A number lock on a suitcase has 3 wheels each labeled with ten digits from 0 to 9. If the opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible?

Find four numbers forming a geometric progression in which the third term is greater than the first term by 9, and the second term is greater than the 4th by 18.

Consider the binomial expansion of (sqrt(x)+(1/(2x^(1/4))))^n n in NN , where the terms of the expansion are written in decreasing powers of x. If the coefficients of the first three terms form an arithmetic progression then the statement(s) which hold good is(are)