The sum of three consecutive terms of an $A.P.$ is $30$ and the product of its first and last term is $75$. Then,the common difference of the $A.P.$ is $\ldots \ldots \ldots \ldots .$

Find whether $55$ is a term of the $AP: 7, 10, 13, \dots$ or not. If yes, find which term it is. (in $^{th}$)

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?

The $A.P.$ with $a = -3$ and $d = -2$ is..........

For an $A.P.$,the $10^{th}$ term is $52$ and the $16^{th}$ term is $82$. Find the $n^{th}$ term and the $32^{nd}$ term of the $A.P.$

Justify whether it is true to say that $-1, -\frac{3}{2}, -2, \frac{5}{2}, \ldots$ forms an $AP$ as $a_{2}-a_{1} = a_{3}-a_{2}$.