A sum of ₹ $\displaystyle 2,000$ is invested at $\displaystyle 7 \%$ per annum simple interest. Calculate the interests at the end of $\displaystyle 1^{\text {st }}, 2^{\text {nd }}$ and $\displaystyle 3^{\text {rd }}$ year. Do these interests form an AP ? If so, find the interest at the end of the $\displaystyle 27{ }^{\text {th }}$ year.

Interest at the end of \(\displaystyle 1^{\text {st }}\) year \(\displaystyle =\frac{2000 \times 7 \times 1}{100}=₹ 140\) Interest at the end of \(\displaystyle 2^{\text {nd }}\) year \(\displaystyle =\frac{2000 \times 7 \times 2}{100}=₹ 280\) Interest at the end of \(\displaystyle 3^{\text {rd }}\) year \(\displaystyle =\frac{2000 \times 7 \times 3}{100}=₹ 420\) $\displaystyle 140$, $\displaystyle 280$, 420... Yes, Interests form an AP with first term = $\displaystyle 140$ and common difference = $\displaystyle 140$ Interest at the end of \(\displaystyle 27{ }^{\text {th }}\) year \(\displaystyle =140+26 \times 140\) \[\text { = ₹ } 3780 \]