If an A.P., a G.P. and a H.P. have the same first term and same `(2n+1)` th term and their `(n+1)^n` terms are a,b,c respectively, then the radius of the circle. `x^2+y^2+2bx+2ky+ac=0` is

If the first and (2n-1)^(th) terms of an A.P,a G.P and an H.P of positive terms are equal and their (n+1)^(th) terms are a,b&c respectively then

An A.P. and a G.P. of positive terms have the same first term and the sum of their first, second and third terms are respectively, 1, 1/2 and 2. Show that the sum of their fourth terms is 19/2

If the 4th and the 7th terms of an H.P. are 1/2 and 2/7 respectively . Find the first term.

If the sum of first n terms of an A.P. is 3n^(2)-2n , then its 19th term is

If a be the first term, b be the nth term and P be the product of n terms of a GP then prove that P^2=(ab)^n .

If the first and the nth terms of a GP are a and b respectively and if P is the product of the first n terms, then P^(2) is equal to

If the n^(th) term of a G.P. is 3 (4^(n+1)) then its first term and common ratio are respectively