Consider an infinite $G.P. $ with first term a and common ratio $r$, its sum is $4$ and the second term is $3/4$, then
$a = \frac{7}{4},\,r = \frac{3}{7}$
$a = \frac{3}{2},\,r = \frac{1}{2}$
$a = 2,\,r = \frac{3}{8}$
$a = 3,\,r = \frac{1}{4}$
The sum of first three terms of a $G.P.$ is $\frac{13}{12}$ and their product is $-1$ Find the common ratio and the terms.
The sum of the first three terms of a $G.P.$ is $S$ and their product is $27 .$ Then all such $S$ lie in
The number of natural number $n$ in the interval $[1005, 2010]$ for which the polynomial. $1+x+x^2+x^3+\ldots+x^{n-1}$ divides the polynomial $1+x^2+x^4+x^6+\ldots+x^{2010}$ is
If $1\, + \,\sin x\, + \,{\sin ^2}x\, + \,...\infty \, = \,4\, + \,2\sqrt 3 ,\,0\, < \,x\, < \,\pi $ then
If $(y - x),\,\,2(y - a)$ and $(y - z)$ are in $H.P.$, then $x - a,$ $y - a,$ $z - a$ are in