Let there be an A.P. with first term $‘a’$, common difference $‘d’$. If $a_n$ denotes its $n^{\text{th}}$ term and $S_n$ the sum of first $n$ terms, find $a$, if $a_n=28$, $S_n=144$ and $n=9$.

Let there be an AP with first term $‘a’$, common difference $‘d’$. If $a_n$ denotes its $n^{\text{th}}$ term and $S_n$ the sum of first $n$ terms, find $n$ and $d$, if $a=8$, $a_n=62$ and $S_n=210$.

Let there be an A.P. with first term $‘a’$, common difference $‘d’$. If $a_n$ denotes its $n^{th}$ term and $S_n$ the sum of first $n$ terms, then find $k$ where $S_n=3n^2+5n$ and $a_k=164$.

Let there be an A.P. with first term $‘a’$, common difference $‘d’$. If $a_n$ denotes its $n^{th}$ term and $S_n$ the sum of first $n$ terms, find.

$S_{22}$, if $d=22$ and $a_{22}=149$