If $\frac{{a + bx}}{{a – bx}} = \frac{{b + cx}}{{b – cx}} = \frac{{c + dx}}{{c – dx}},\left( {x \ne 0} \right)$ then $a$, $b$, $c$, $d$ 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 :-

If the sum of $n$ terms of a $G.P.$ is $255$ and ${n^{th}}$ terms is $128$ and common ratio is $2$, then first term will be

If $n$ geometric means be inserted between $a$ and $b$ then the ${n^{th}}$ geometric mean will be

For a sequence $ < {a_n} > ,\;{a_1} = 2$ and $\frac{{{a_{n + 1}}}}{{{a_n}}} = \frac{1}{3}$. Then $\sum\limits_{r = 1}^{20} {{a_r}} $ is