In an $AP$,given $l = 28$,$S = 144$,and there are a total of $9$ terms. Find $a$.

In a potato race,a bucket is placed at the starting point,which is $5\, m$ from the first potato,and the other potatoes are placed $3\, m$ apart in a straight line. There are ten potatoes in the line. $A$ competitor starts from the bucket,picks up the nearest potato,runs back with it,drops it in the bucket,runs back to pick up the next potato,runs to the bucket to drop it in,and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run? (in $m$)

Subba Rao started work in $1995$ at an annual salary of ₹ $5000$ and received an increment of ₹ $200$ each year. In which year did his income reach ₹ $7000$?

The sum of the third and the seventh terms of an $AP$ is $6$ and their product is $8$. Find the sum of the first sixteen terms of the $AP$.

Find the sum of the first $40$ positive integers divisible by $6$.

For the $AP: \frac{3}{2}, \frac{1}{2}, -\frac{1}{2}, -\frac{3}{2}, \ldots,$ write the first term $a$ and the common difference $d$.