**Q) In which of the following situations does the list of numbers involved make an arithmetic progression and why?
(iv) The amount of money in the account every year, when Rs. 10,000 is deposited at compound interest at 8% per annum..**

**Ans: **Let’s start from making a sequence of the air amount in the cylinder after every stroke and then check if the sequence makes an AP or not.

Initial amount given as Rs. 10,000

Clearly this becomes our 1^{st} term,

Next, we know that the amount growing at compound interest is calculated by:

Here, S = Amount after compound interest

P = Principal amount

r = rate of interest

n = number of times interest is compounded

Let’s calculate amount after 1^{st} year

Here it is given, P = 10,000, r = 8 (rate of interest is 8%) and since we are calculating after one year, therefore, n =1

This becomes our 2^{nd }term,

Further, let’s calculate amount after 2^{nd} year

Here it is given, P = 10,000, r = 8 (rate of interest is 8%) and since we are calculating after 2 years, therefore, n =2

This becomes our 3^{rd }term,

Thus, the sequence starts to emerge as 10,000; 10,800; 11,664;……

Next, let’s check the difference between 2 sets of consecutive terms:

Difference between 1^{st} two terms:

Similarly, difference between next two terms:

**Here, since the difference between any two consecutive terms is not equal, hence the sequence formed is not an AP**

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