In an $AP$, the first term is $2$, the last term is $29$ and the sum of all the terms is $155$. Find the common difference.

In an $AP$, the first term is $-4$, the last term is $29$ and the sum of all its terms is $150$. Find its common difference.

The first and the last terms of an $AP$ are $17$ and $350$ respectively. If the common difference is $9$, how many terms are there and what is their sum?

The first and last terms of an $AP$ are $5$ and $45$ respectively. If the sum of all its terms is $400$, find the common difference and the number of terms.

The ${12}^{th}$ term of an $AP$is $-13$ and the sum of its first four terms is $24$. Find the sum of its first $10$ terms.

The sum of the first $7$ terms of an $AP$ is $182$. If its $4^{th}$ and ${17}^{th}$ terms are in the ratio $1:5$, find the $AP$.

The sum of the first $9$ terms of an $AP$ is $81$ and that of its first $20$ terms is $400$. Find the first term and common difference of the $AP.$

The sum of the first $7$ terms of an $AP$ is $49$ and the sum of its first$17$term is$289$. Find the sum of its first $n$ terms.