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A sum of ₹2,000 is invested at $7\%$ per annum simple interest. Calculate the interests at the end of $1^{st}$, $2^{nd}$ and $3^{rd}$ year. Do these interests form an AP ? If so, find the interest at the end of the $27^{th}$ year.
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Interest at the end of $1^{st}$ year $= \frac{2000 \times 7 \times 1}{100} = \text{Rs}140$
Interest at the end of $2^{nd}$ year $= \frac{2000 \times 7 \times 2}{100} = \text{Rs}280$
Interest at the end of $3^{rd}$ year $= \frac{2000 \times 7 \times 3}{100} = \text{Rs}420$
$140, 280, 420, \dots$
Yes, Interests form an AP with first term = $140$ and common difference = $140$
Interest at the end of $27^{th}$ year $= 140 + 26 \times 140$
$= \text{Rs}3780$
Interest at the end of $2^{nd}$ year $= \frac{2000 \times 7 \times 2}{100} = \text{Rs}280$
Interest at the end of $3^{rd}$ year $= \frac{2000 \times 7 \times 3}{100} = \text{Rs}420$
$140, 280, 420, \dots$
Yes, Interests form an AP with first term = $140$ and common difference = $140$
Interest at the end of $27^{th}$ year $= 140 + 26 \times 140$
$= \text{Rs}3780$