$\,9.\,$ In an infinite geometric G.P., each term is equal to three times the sum of all the terms that follow it and…

$\,3.\,$ Express $\,0.\overline{4}\,\,$ as an infinite geometric series and hence prove that $\,\,(0.444\cdots)^{1/2}…

$\,1.\,$ Find the sum of each f the following infinite geometric series, if it exists : $\,(i)\,1+\frac 13+\frac 19+\f…

$\,1.\,$ If $\,5,x,y,z,405\,\,$ are the first five terms of a G.P., find the values of $\,\,x,y,z.$ Sol.  Clearly in …

$\,24.\,$ If $\,a\,$ is A.M. of two positive numbers $\,b\,$ and $\,c\,$ and two G.M.'s between $\,b\,$ and $\,c\…

$\,18.\,$ If $\,p, q, r\,$ be in arithmetic progression, then show that the $\,p\,$th, $\,q\,$th and $\,r\,$th terms …

$\,11.\,$ A boy saves $\,1\,$ paisa the first day, $\,2\,$ paise the second day, $\,4\,$ paise the third day and $\,8…

$\,7.\,$ If the $\,n\,$th term of the series be $\,(2 \cdot 3^{n-1}+1),\,$ find the sum of first $\,r\,$ terms of the…

$\,5(i)\,$ Find three numbers in G.P. whose sum is $\,19\,$ and product is $\,216\,$. Sol.  Let the three numbers in …

$\,1.\,$ The common ratio of a series in G.P. is $\,3;\,$ the sum of the $\,1\,$st and $\,3\,$rd terms is equal to th…