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Q.

The income of a person is Rs. 3,00,000 in the first year and he receives an increase of Rs. 10,000 to his income per year for the next 19 years, then the total amount he received in 20 years is ____.

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Detailed Solution

The income of a person is Rs. 3,00,000 in the first year and he receives an increase of Rs. 10,000 to his income per year for the next 19 years, then the total amount he received in 20 years is 79,00,000.
We know,

S n = n 2 2 a + n − 1 d .

Where,
The first term is a.
The common difference is d.
The number of terms are n.
The first-year income of a person is 3,00,000.
The A.P with the first term 3,00,000 and the common difference 10,000 will be 300000, 310000, 320000, 330000…...
Therefore,

S n = n 2 2 a + n − 1 d ⇒ S 20 = 202 2 × 300000 + 20 − 1 10000 ⇒ S 20 = 10 600000 + 190000 ⇒ S 20 = 7900000

Therefore, the total number of amounts a person received was 79,00,000.

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The income of a person is Rs. 3,00,000 in the first year and he receives an increase of Rs. 10,000 to his income per year for the next 19 years, then the total amount he received in 20 years is ____.