Question 1

In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?

(i) The taxi fare after each km when the fare is $\text{₹ } 15$ for the first km and $\text{₹ } 8$ for each additional km.

(ii) The amount of air present in a cylinder when a vacuum pump removes $\dfrac{1}{4}$ of the air remaining in the cylinder at a time.

(iii) The cost of digging a well after every metre of digging, when it costs $\text{₹ } 150$ for the first metre and rises by $\text{₹ } 50$ for each subsequent metre.

(iv) The amount of money in the account every year, when $\text{₹ } 10000$ is deposited at compound interest at $8\%$ per annum.