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 four arithmetic means between $3$ and $23$ are

Write down the $5^{th}$ term of the series $\frac{1}{4} - \frac{1}{2} + 1 \ldots$

If $\log 2, \log (2^{x}-1)$ and $\log (2^{x}+3)$ (all to the base $10$) are three consecutive terms of an Arithmetic Progression,then the value of $x$ is equal to

If the harmonic mean between $a$ and $b$ is $H$,then the value of $\frac{1}{H - a} + \frac{1}{H - b}$ is

Given an $A.P.$ whose terms are all positive integers. The sum of its first nine terms is greater than $200$ and less than $220$. If the second term in it is $12$,then its $4^{th}$ term is