If the ${4^{th}},\;{7^{th}}$ and ${10^{th}}$ terms of a $G.P.$ be $a,\;b,\;c$ respectively, then the relation between $a,\;b,\;c$ is
$b = \frac{{a + c}}{2}$
${a^2} = bc$
${b^2} = ac$
${c^2} = ab$
The third term of a $G.P.$ is the square of first term. If the second term is $8$, then the ${6^{th}}$ term is
Suppose four distinct positive numbers $a_1, a_2, a_3, a_4$ are in $G.P.$ Let $b_1=a_1, b_2=b_1+a_2, b_3=b_2+a_3$ and $b_4=b_3+a_4$.
$STATEMENT-1$ : The numbers $\mathrm{b}_1, \mathrm{~b}_2, \mathrm{~b}_3, \mathrm{~b}_4$ are neither in $A.P$. nor in $G.P.$ and
$STATEMENT-2$ : The numbers $\mathrm{b}_1, \mathrm{~b}_2, \mathrm{~b}_3, \mathrm{~b}_4$ are in $H.P.$
The sum of $100$ terms of the series $.9 + .09 + .009.........$ will be
Insert two numbers between $3$ and $81$ so that the resulting sequence is $G.P.$