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 Rs.$15$ for the first km and Rs. $8$ for each additional km.
(ii) The amount of air present in a cylinder when a vacuum pump removes $\frac{1}{4}$ 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 Rs. $150$ for the first metre and rises by Rs. $50$ for each subsequent metre.
(iv) The amount of money in the account every year, when Rs. $10000$ is deposited at compound interest at $8$ % per annum.

Here, each subsequent term is not obtained by adding a fixed number to the previous term.

Hence, it is not an AP.

(iii) Cost of digging of $1^{st}$ meter $=150$

Cost of digging of $2^{nd}$ meter $=150+50=200$

Cost of digging of $3^{rd}$ meter $=200+50=250$

Here, each subsequent term is obtained by adding a fixed number $(50)$ to the previous term.

Hence, it is an AP.

(iv)  Amount in the beginning $=$ Rs. $10000$

Interest at the end of $1^{st}$ year @ $8\%$ = $10000\times 8$ 

Thus, amount at the end of $1^{st}$ year $=10000+800=10800$

Interest at the end of $2^{nd}$ year @ $8\%$ = $10800\times 8$

Thus, amount at the end of $2^{nd}$ year $=10800+864=11664$

Since, each subsequent term is not obtained by adding a fixed number to the previous term; hence, it is not an AP.