The $n^{th}$ term of an $A.P.$ is given by $T_n = 5n - 2$. Then,the $12^{th}$ term of the $A.P.$ is:

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.

Which of the following sequences is an $A.P.$?

$7+12+17+\ldots+102 = \ldots$

Divya deposited $Rs. 1000$ at compound interest at the rate of $10\%$ per annum. The amounts at the end of the first year,second year,third year,$\ldots,$ form an $AP$. Justify your answer.

For any $A.P.$,$T_{30} - T_{20} = \ldots \ldots \ldots \ldots$