State whether the list of numbers in the following situation is an $A . P .$
Divya deposited $R s . 1000$ as compound interest at the rate of $10 %$ per annum. The amount at the end of first year, second year, third year,. and so on.

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Solution

Principal $=$ Rs. $1000$
Rate of interest $= 10 %$ pa
The amount after $1$ st year $(A_{1}) = P {(1 + \frac{r}{100})}^{1}$
$= 1000 (1 + \frac{10}{100})$
$=$ Rs. $1100$

After $2^{n d}$ year $(A_{2}) = A_{1} (1 + \frac{r}{100})$
$= 1100 \times \frac{11}{10}$
$=$ Rs. $1210$

After third year $(A_{3}) =$ Rs. $1210 (1 + \frac{10}{100})$
$=$ Rs. $1331$

These numbers does not form AP.

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