A manufacturer of TV sets produced $600$ sets in the third year and $700$ sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find the number of TV sets produced in the $1^{st}$ year.

Find the next three terms of the arithmetic progressions given below:

$5, 11, 17, 23,...........$

Form an infinite arithmetic progressions where the first term is $5$ and common difference is $3$.

Form two finite arithmetic progressions each having $5$ terms.

$200$ logs are stacked in the following manner: $20$ logs in the bottom row, $19$ in the next row, $18$ in the row next to it and so on (see figure).

Find out in how many rows the $200$ logs placed and how many logs are in the top row?

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 (see figure).

A competitor starts from a bucket, picks up the nearest potato, run back with it, drops it in the bucket, run 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 meters?