First term n - th term and product of first n term be a , b and p respectively of a G .P . Then show that `p^(2)=(ab)^(n)` .

If a be the first term, l the nth and p the product of first n terms of a G.P. show that, p^(2) = (al)^(n) .

If the first and the n^("th") term of a G.P. are a and b, respectively, and if P is the product of n terms, prove that P^2 = (ab)^n .

If the first term, common ratio and the sum of first n terms of a G.P. be a, r and S_(n) respectively, find the value of S_(1) + S_(2) + S_(3) +….+S_(n) .

If 5^(th) term of a G.P. is 2 and product of first 9 terms is 298 K, then the value of K is -

If the first and the nth terms of a G.P are a and b , respectively, and if P is the product of the first n terms then prove that P^2=(a b)^ndot

The first and the last terms of a G.P are a and k respectively if the number of terms be n prove that n=1+(logk-loga)/(logr) where r is the common ratio

The first two term of a G.P are 125, and 25 respectively. Find the 5th and 6th term of the GP.

If the 5th term of a G.P. is x, then the product of its first nine terms is-

Find the n th term and the sum of first n terms of thefollowing sequence 2,7,20,57,166,..

If S be the sum of first (2n+1) terms of an A.P and the sum of terms in odd positions of these (2n+1) terms be S', then show that (n+1)S = (2n+1)S'.