In which of the following situations, does the list of numbers involved make an arithmetic progression and why?
The amount of money in the account every year, when Rs. 10000 is deposited at compound interest at 8% per annum.
Given:
The amount of money in the account every year, when Rs. 10000 is deposited at compound interest at 8% per annum.
To do:
We have to check whether the sequence formed by the above information is an A.P.
Solution:
Let
$a_1 = Rs.\ 10000$
This implies,
$a_2 = Rs.\ 10000 + Rs.\ 10000 \times \frac{8}{100}$
$= Rs.\ 10000 + Rs.\ 800$
$= Rs.\ 10800$
$a_3 = Rs.\ 10800 + Rs.\ 10800 \times 8100$
$= Rs.\ 10800 + Rs.\ 864$
$= Rs.\ 11664$
$a_2 - a_1 = Rs.\ 10800 - Rs.\ 10000$
$= Rs.\ 800$
$a_3 - a_2 = Rs.\ 11664 - ₹ 10800$
$= Rs.\ 864$
$a_3 - a_2 ≠ a_2 - a_1$
Therefore, the given information does not form an A.P.
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