Let $a_{1}, a_{2}, a_{3}, \ldots$ be a G.P. such that $a_{1}<0$; $a_{1}+a_{2}=4$ and $a_{3}+a_{4}=16 .$ If $\sum\limits_{i=1}^{9} a_{i}=4 \lambda,$ then $\lambda$ is equal to 

If the sum of the $n$ terms of $G.P.$ is $S$ product is $P$ and sum of their inverse is $R$, than ${P^2}$ is equal to

The geometric series $a + ar + ar^2 + ar^3 +..... \infty$ has sum $7$ and the terms involving odd powers of $r$ has sum $'3'$, then the value of $(a^2 -r^2)$ is -

The sum of the $3^{rd}$ and the $4^{th}$ terms of a $G.P.$ is $60$ and the product of its first three terms is $1000$. If the first term of this $G.P.$ is positive, then its $7^{th}$ term is

An $A.P.$, a $G.P.$ and a $H.P.$ have the same first and last terms and the same odd number of terms. The middle terms of the three series are in

In an increasing geometric progression ol positive terms, the sum of the second and sixth terms is $\frac{70}{3}$ and the product of the third and fifth terms is $49$. Then the sum of the $4^{\text {th }}, 6^{\text {th }}$ and $8^{\text {th }}$ terms is :-