Question 1 (iii)
In which of the following situations does the list of numbers involved make an arithmetic progression and why?
(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.

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Solution

Cost of digging first metre = Rs. 150
Cost of digging first 2 metres = 150 + 50 = Rs. 200
Cost of digging first 3 metres = 200 + 50 = Rs. 250
Cost of digging first 4 metres = 250 + 50 = Rs. 300
Clearly; 150, 200, 250, 300 … forms an A.P. because every term is 50 more than the preceding term.

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

In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?
(i) The taxi fare after each $k m$ when the fare is $R s .15$ for the first $k m$ and $R s .8$ for each additional $k m$ .
(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 $R s .150$ for the first metre and rises by $R s .50$ for each subsequent metre.
(iv) The amount of money in the account every year, when $R s .10000$ is deposited at compound interest at $8 %$ per annum.

In which of the following situations, does the list of numbers involved make as 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 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.

In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?
(i)The amount of air present in a cylinder when a vacuum pump removes ( $\frac{1}{4})^{t h}$ of the air remaining in the cylinder at a time.
(ii)The cost of digging a well after every meter of digging, when it costs Rs 150 for the first meter and rises by Rs 50 for each subsequent meter.