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Question
The income of a person is Rs 300,000 in the first year and he receives an increase of Rs 10000 to his income per year for the next 19 years. Find the total amount, he received in 20 years.
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Solution
Let
\[S_n\] denote the total amount the person receives in n years.
Let d be the common increment in his income every year.
Let a denote the initial income of the person.
Here, a = 300,000, d = 10000, n = 20
Total amount at the end of 20 years:
\[S_{20} = \frac{20}{2}\left\{ 2 \times 300, 000 + (20 - 1)10, 000 \right\}\]
\[ = 79, 00, 000\]
Therefore, the total amount the person receives in 20 years is Rs 79,00,000.
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