If $n$ geometric means be inserted between $a$ and $b$ then the ${n^{th}}$ geometric mean will be
$a\,{\left( {\frac{b}{a}} \right)^{\frac{n}{{n - 1}}}}$
$a\,{\left( {\frac{b}{a}} \right)^{\frac{{n - 1}}{n}}}$
$a\,{\left( {\frac{b}{a}} \right)^{\frac{n}{{n + 1}}}}$
$a\,{\left( {\frac{b}{a}} \right)^{\frac{1}{n}}}$
If $a,\;b,\;c$ are in $A.P.$, then ${10^{ax + 10}},\;{10^{bx + 10}},\;{10^{cx + 10}}$ will be in
If $a,\;b,\;c$ are in $G.P.$, then
If $(y - x),\,\,2(y - a)$ and $(y - z)$ are in $H.P.$, then $x - a,$ $y - a,$ $z - a$ are in
Show that the products of the corresponding terms of the sequences $a,$ $ar,$ $a r^{2},$ $......a r^{n-1}$ and $A, A R, A R^{2}, \ldots, A R^{n-1}$ form a $G .P.,$ and find the common ratio.
If the ratio of the sum of first three terms and the sum of first six terms of a $G.P.$ be $125 : 152$, then the common ratio r is