The income of a person is Rs. ,3,00,000 in th | vedclass

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(A) The income follows an arithmetic progression $(A.P.)$ where the first term $a = 3,00,000$,the common difference $d = 10,000$,and the number of yea

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$Rs. \,79,00,000$

Vedclass · Answer

(A) The income follows an arithmetic progression $(A.P.)$ where the first term $a = 3,00,000$,the common difference $d = 10,000$,and the number of years $n = 20$. The sum of the first $n$ terms of an $A.P.$ is given by the formula: $S_n = \frac{n}{2} [2a + (n - 1)d]$. Substituting the values: $S_{20} = \frac{20}{2} [2(3,00,000) + (20 - 1)(10,000)]$ $S_{20} = 10 [6,00,000 + 19(10,000)]$ $S_{20} = 10 [6,00,000 + 1,90,000]$ $S_{20} = 10 [7,90,000] = 79,00,000$. Thus,the total amount received in $20$ years is $Rs. \,79,00,000$.

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. Find the total amount he received in $20$ years.

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