If $\frac{{3 + 5 + 7 + ..........{\rm{to}}\;n\;{\rm{terms}}}}{{5 + 8 + 11 + .........{\rm{to}}\;10\;{\rm{terms}}}} = 7$, then the value of $n$ is

The number of terms of the $A.P. 3,7,11,15...$ to be taken so that the sum is $406$ is

If the sum of the first $2n$ terms of $2,\,5,\,8...$ is equal to the sum of the first $n$ terms of $57,\,59,\,61...$, then $n$ is equal to

The number of terms common to the two A.P.'s $3,7,11, \ldots ., 407$ and $2,9,16, \ldots . .709$ is

The sum of all the elements in the set $\{\mathrm{n} \in\{1,2, \ldots \ldots ., 100\} \mid$ $H.C.F.$ of $n$ and $2040$ is $1\,\}$ is equal to $.....$

The sums of $n$ terms of two arithmatic series are in the ratio $2n + 3:6n + 5$, then the ratio of their ${13^{th}}$ terms is