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

(i) 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.

(ii) The amount of money in the account every year, when Rs 10000 is deposited at compound interest at 8% per annum.

Solution(i):

The provided condition can be written as follows:

Cost of digging a well for the first metre = Rs.150

Digging a well for the first 2 metres costs Rs.150+50 = Rs.200.

Digging a well for the first 3 metres costs Rs.200+50 = Rs.250.

Digging a well for the first 4 metres costs Rs.250+50 = Rs.300.

And so forth.

Solution(ii):

We know that if Rs. P is deposited for n years at r percent compound interest, the total amount will be:

P(1+r/100)n

As a result, at the end of each year, the quantity of money will be:

10000(1+8/100), 10000(1+8/100)2, 10000(1+8/100)3……

Clearly, there is no common distinction between the terms in this sequence. As a result, this isn’t an A.P.