If the $7^{th}$ term of an Arithmetic Progression $(AP)$ is $40$,then the sum of its first $13$ terms is........

If $100$ times the $100^{th}$ term of an Arithmetic Progression with a non-zero common difference is equal to $50$ times its $50^{th}$ term,then what is its $150^{th}$ term?

If $x, y, z$ are three real numbers with the same sign,then the value of $\frac{x}{y} + \frac{y}{z} + \frac{z}{x}$ lies in which interval?

If the roots of the equation $x^{3}+a x^{2}+b x+c=0$ are in $AP$,then $2 a^{3}-9 a b$ is equal to (in $c$)

If $a^2, b^2, c^2$ are in $A.P.$,then $(b + c)^{-1}, (c + a)^{-1}$ and $(a + b)^{-1}$ will be in

The number of terms in an $A.P.$ is even. The sum of the odd terms is $24$ and the sum of the even terms is $30$. If the last term exceeds the first term by $10\frac{1}{2}$,then the number of terms in the $A.P.$ is: