The $8^{\text {th }}$ common term of the series $S _1=3+7+11+15+19+\ldots . .$ ; $S _2=1+6+11+16+21+\ldots .$ is $.......$.

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

If the sum of the $10$ terms of an $A.P.$ is $4$ times to the sum of its $5$ terms, then the ratio of first term and common difference is

Write the first five terms of the sequences whose $n^{t h}$ term is $a_{n}=\frac{2 n-3}{6}$

If the $10^{\text {th }}$ term of an A.P. is $\frac{1}{20}$ and its $20^{\text {th }}$ term is $\frac{1}{10},$ then the sum of its first $200$ terms is

If $n$ arithmetic means are inserted between a and $100$ such that the ratio of the first mean to the last mean is $1: 7$ and $a+n=33$, then the value of $n$ is