In which of the following situations, the sequence of numbers formed will form an A.P. ?pya deposited Rs. 1000 at compound interest at the rate of 10% per annum. The amount at the end of first year, second year, third year, …, and so on.
Given:
Divya deposited Rs. 1000 at compound interest at the rate of 10% per annum.
To do:
We have to check whether the sequence formed by the above information is an A.P.
Solution:
The amount at the end of the first year $=Rs.\ 1000(1+\frac{10}{100})^1=Rs.\ 1000\times1.1=Rs.\ 1100$
The amount at the end of the second year $=Rs.\ 1000(1+\frac{10}{100})^2=Rs.\ 1000\times(1.1)^2=Rs.\ 1210$
The amount at the end of the third year $=Rs.\ 1000(1+\frac{10}{100})^3=Rs.\ 1000\times(1.1)^3=Rs.\ 1331$
The sequence formed by the amounts(in Rupes) at the end of each year is as follows:
$1100, 1210, 1331, .......$
$1210-1100=110$, $1331-1210=121$
$110≠121$
Therefore, the sequence of the numbers does not form an A.P.  
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