If the sum of the first $40$ terms of the series $3+4+8+9+13+14+18+19+\ldots$ is $(102)m$,then $m$ is equal to:

The sum of the infinite series $\frac{1}{9} + \frac{1}{18} + \frac{1}{30} + \frac{1}{45} + \frac{1}{63} + ..........\infty$ is equal to :-

If $x > 1, y > 1, z > 1$ are in $G.P.$,then $\frac{1}{1 + \log x}, \frac{1}{1 + \log y}, \frac{1}{1 + \log z}$ are in

$A$ man saves $200$ in each of the first three months of his service. In each of the subsequent months,his saving increases by $40$ more than the saving of the immediately previous month. His total saving from the start of service will be $11040$ after ............ months.

The difference between the fourth term and the first term of a Geometric Progression is $52.$ If the sum of its first three terms is $26,$ then the sum of the first six terms of the progression is

If the ${5^{th}}$ term of a $H.P.$ is $\frac{1}{45}$ and the ${11^{th}}$ term is $\frac{1}{69}$,then its ${16^{th}}$ term will be: