Find the $31^{st}$ term of an $AP$ whose $11^{th}$ term is $38$ and the $16^{th}$ term is $73.$

Write the first four terms of the $AP,$ when the first term $a$ and the common difference $d$ are given as follows: $a = -1, d = \frac{1}{2}$

$a, 2a, 3a, 4a, \dots$ are $APs$? If they form an $AP,$ find the common difference $d$ and write three more terms.

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 $m$)

Are $-\frac{1}{2}, -\frac{1}{2}, -\frac{1}{2}, -\frac{1}{2}, \ldots$ in an $AP$? If they form an $AP$,find the common difference $d$ and write three more terms.

Do $1, 1, 1, 2, 2, 2, 3, 3, 3, \ldots$ form an $AP$? If they form an $AP$,write the next two terms.