$A$ 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 ${20^{th}}$ term of the series $2 \times 4 + 4 \times 6 + 6 \times 8 + \dots$ will be

The value of $\sum_{n=0}^{\infty} \frac{(n+1)^2}{7^n}$ is -

$A$ person is to count $4500$ currency notes. Let $a_n$ denote the number of notes he counts in the $n^{th}$ minute. If $a_1 = a_2 = \ldots = a_{10} = 150$ and $a_{10}, a_{11}, \ldots$ are in an $A.P.$ with common difference $-2$,then the time taken by him to count all notes is ............... minutes.

In a $H.P.$,the $p^{th}$ term is $q$ and the $q^{th}$ term is $p$. Then the $pq^{th}$ term is:

The number of terms common between the two series $2 + 5 + 8 + \dots$ up to $50$ terms and the series $3 + 5 + 7 + 9 + \dots$ up to $60$ terms is: