Determine $k$ so that $k^{2}+4k+8, 2k^{2}+3k+6, 3k^{2}+4k+4$ are three consecutive terms of an $AP$.

The $7^{th}$ and $12^{th}$ terms of an $A.P.$ are $46$ and $71$ respectively. Find the $n^{th}$ term of the $A.P.$

For a given $A.P.$,the first term is $7$ and the $10^{th}$ term is $61$. Find the common difference of the $A.P.$ and its $25^{th}$ term.

Which term of the $A.P.$ $4, 9, 14, \ldots$ is $224$ (in $^{th}$)?

The $n^{th}$ term of an $A.P.$ is given by $T_{n} = -4n + 15$. Find the $15^{th}$ term and the common difference of the $A.P.$

To clear a debt,Ajaybhai has to pay $Rs. 100$ in the first monthly instalment,$Rs. 150$ in the second monthly instalment,and onwards he has to pay in each monthly instalment $Rs. 50$ more than what was paid in the previous instalment. He has to pay $24$ monthly instalments in all. What amount will he pay in the $24^{th}$ instalment?