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Question
A man saved Rs 16500 in ten years. In each year after the first he saved Rs 100 more than he did in the receding year. How much did he save in the first year?
Solution
Let the amount saved by the man in the first year be Rs A.
Let d be the common difference.
Let \[S_{10}\] denote the amount he saves in ten years.
Here, n =10, d =100
We know:
\[S_n = \frac{n}{2}\left\{ 2A + \left( n - 1 \right)d \right\}\]
\[ \therefore S_{10} = \frac{10}{2}\left\{ 2A + \left( 10 - 1 \right)100 \right\}\]
\[ \Rightarrow 16500 = 5\left\{ 2A + 900 \right\}\]
\[ \Rightarrow 3300 = 2A + 900\]
\[ \Rightarrow A = 1200\]
Therefore, the man saved Rs 1200 in the first year.
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