Find the sum of the first $30$ terms of the $A.P.$ $15, 20, 25, \ldots$

In the $AP: 10, 5, 0, -5, \ldots$,the common difference $d$ is equal to $5$. Justify whether the above statement is true or false.

The sum of three numbers in $A.P.$ is $21$. The product of the first and the third number exceeds the second number by $6$. Find those numbers.

Verify that each of the following is an $AP$,and then write its next three terms.
$a+b, (a+1)+b, (a+1)+(b+1), \ldots$

Determine the $AP$ whose fifth term is $19$ and the difference of the eighth term from the thirteenth term is $20$.

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?