₹ 2,000 is invested at 10 percent simple interest. Check at the end of the every year whether the interest amount is in A.P. or not. If this is an A.P., then find interest amount after 10 years.

Answer: Yes, the interest amounts form an A.P. with \(a = 200\), \(d = 200\); interest after 10 years = ₹ 2,000.

SI for one year \(= \dfrac{2000 \times 10 \times 1}{100} = \) ₹ 200.

Interest at the end of 1st year = ₹ 200, at the end of 2nd year = ₹ 400, at the end of 3rd year = ₹ 600, and so on.

\(400 - 200 = 200\) and \(600 - 400 = 200\), so the difference is constant : it is an A.P. with \(a = 200\), \(d = 200\).

Interest after 10 years \(= t_{10} = a + 9d = 200 + 9(200) = \) ₹ 2,000.