Show that in an infinite G.P. with common ratio `r(|r|<1)` , each term bears a constant ratio to the sum of all terms that follow it.

Prove that in an infinite G.P. whose common ratio r is numerically less than one, the ratio of any term to the sum of all the succeeding terms is (1-r)/r

The sum of an infinite G.P. whose common ratio is numerically less than 1 is 32 and the sum of the first two terms is 24. Find the terms of G.P.

If the sides of triangle ABC are in G.P with common ratio r (r<1) , show that r<1/2(sqrt5+1)

if (a,b) , (c,d) , (e,f) are the vertices of a triangle such that a, c, e are in GP . with common ratio r and b, d, f are in GP with common ratio s , then the area of the triangle is

If a ,b ,c are in G.P. with common ratio r_1a n dalpha,beta,gamma are in G.P. with common ratio r_2 and equations a x+alphay+z=0,b x+betay+z=0,c x+gammay+z=0 have only zero solution, then which of the following is not true?

If a ,b ,c are in G.P. with common ratio r_1a n dalpha,beta,gamma are in G.P. with common ratio r_2 and equations a x+alphay+z=0,b x+betay+z=0,c x+gammay+z=0 have only zero solution, then which of the following is not true? a. a+b+c b. a b c c. 1 d. none of these

Statement 1: If an infinite G.P. has 2nd term x and its sum is 4, then x belongs to (-8,1)dot Statement 2: Sum of an infinite G.P. is finite if for its common ratio r ,0<|r|<1.

If there be n quantities in G.P., whose common ratio is r and S_(m) denotes the sum of the first m terms, then the sum of their products, taken two by two, is

Let a_(1),a_(2),a_(3) , be three positive numbers which are G.P. with common ratio r. The inequality a_(3) gt a_(2) + 2a_(1) do not holds if r is equal to

Area of the triangle with vertices (a, b), (x_1,y_1) and (x_2, y_2) where a, x_1,x_2 are in G.P. with common ratio r and b, y_1, y_2 , are in G.P with common ratio s, is