For any three positive real numbers $a,b,c$ ; $9\left( {25{a^2} + {b^2}} \right) + 25\left( {{c^2} - 3ac} \right) = 15b\left( {3a + c} \right)$ then
$a,b,c$ are in $G.P.$
$b,c,a$ are in $G.P.$
$b,c,a$ are in $A.P.$
$a,b,c$ are in $A.P.$
Find the $7^{\text {th }}$ term in the following sequence whose $n^{\text {th }}$ term is $a_{n}=\frac{n^{2}}{2^{n}}$
The number of terms of the $A.P. 3,7,11,15...$ to be taken so that the sum is $406$ is
The ratio of sum of $m$ and $n$ terms of an $A.P.$ is ${m^2}:{n^2}$, then the ratio of ${m^{th}}$ and ${n^{th}}$ term will be
The houses on one side of a road are numbered using consecutive even numbers. The sum of the numbers of all the houses in that row is $170$ . If there are at least $6$ houses in that row and $a$ is the number of the sixth house, then
The sum of the numbers between $100$ and $1000$, which is divisible by $9$ will be