The first four terms of an $AP,$ whose first term is $-2$ and the common difference is $-2,$ are

For a given $A.P.$,the $5^{th}$ term is $30$ and the $12^{th}$ term is $65$. Find the sum of first $30$ terms of this $A.P.$

The sum of four consecutive numbers in an $AP$ is $32$ and the ratio of the product of the first and the last terms to the product of the two middle terms is $7: 15$. Find the numbers.

Is $0$ a term of the $AP : 31, 28, 25, \ldots ?$ Justify your answer.

Determine whether the following sequence is an $A.P.$ or not. (Assume that the pattern continues.) If it is an $A.P.$,find its $n^{th}$ term: $111, 107, 103, 99, \ldots$

Determine whether the following sequence is an $A.P.$ or not. (Assume that the pattern continues.) If it is an $A.P.$,find its $n^{th}$ term: $1, 4, 9, 16, \ldots $