If $A = 1 + {r^z} + {r^{2z}} + {r^{3z}} + .......\infty $, then the value of $r$ will be
$A{(1 - A)^z}$
${\left( {\frac{{A - 1}}{A}} \right)^{1/z}}$
${\left( {\frac{1}{A} - 1} \right)^{1/z}}$
$A{(1 - A)^{1/z}}$
The first two terms of a geometric progression add up to $12.$ the sum of the third and the fourth terms is $48.$ If the terms of the geometric progression are alternately positive and negative, then the first term is
A person has $2$ parents, $4$ grandparents, $8$ great grandparents, and so on. Find the number of his ancestors during the ten generations preceding his own.
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 sum of the first five terms of the series $3 + 4\frac{1}{2} + 6\frac{3}{4} + ......$ will be
Which term of the $GP.,$ $2,8,32, \ldots$ up to $n$ terms is $131072 ?$