If the sum of an infinite $G.P.$ and the sum of square of its terms is $3$, then the common ratio of the first series is
$1$
$\frac{1}{2}$
$\frac{2}{3}$
$\frac{3}{2}$
The sum of few terms of any ratio series is $728$, if common ratio is $3$ and last term is $486$, then first term of series will be
How many terms of the $G.P.$ $3, \frac{3}{2}, \frac{3}{4}, \ldots$ are needed to give the sum $\frac{3069}{512} ?$
Ten trucks, numbered $1$ to $10$ , are carrying packets of sugar. Each packet weights either $999\,g$ or $1000\,g$ and each truck carries only the packets equal weights. The combined weight of $1$ packet selected from the first truck,$2$ packets from the second,$4$ packets from the third, and so on, and $2^9$ packet from the tenth truck is $1022870\,g$. The trucks that have the lighter bags are
Find the $20^{\text {th }}$ and $n^{\text {th }}$ terms of the $G.P.$ $\frac{5}{2}, \frac{5}{4}, \frac{5}{8}, \ldots$
If the sum of an infinite $G.P.$ be $9$ and the sum of first two terms be $5$, then the common ratio is