If ${m^{th}}$ terms of the series $63 + 65 + 67 + 69 + .........$ and $3 + 10 + 17 + 24 + ......$ be equal, then $m = $

Between $1$ and $31, m$ numbers have been inserted in such a way that the resulting sequence is an $A. P.$ and the ratio of $7^{\text {th }}$ and $(m-1)^{\text {th }}$ numbers is $5: 9 .$ Find the value of $m$

If the sum of the first $n$ terms of a series be $5{n^2} + 2n$, then its second term is

If the first term of an $A.P.$ is $3$ and the sum of its first $25$ terms is equal to the sum of its next $15$ terms, then the common difference of this $A.P.$ is :

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

The $20^{\text {th }}$ term from the end of the progression $20,19 \frac{1}{4}, 18 \frac{1}{2}, 17 \frac{3}{4}, \ldots .,-129 \frac{1}{4}$ is :-