Question

the income of the person is rs 3,00,000 in the first year and he receives an increase of rs 10,00 to his income per year for the next 19 years find the total amount he received in 20 years​

Answer 1

Question:

the income of the person is rs 3,00,000 in the first year and he receives an increase of rs 10,00 to his income per year for the next 19 years find the total amount he received in 20 years

Solution

Income of the person in 1st year = Rs 3,00,000

Income of the person in 2nd year = Rs3,00,000 + 10,000

⁣           ⁣          = Rs 3,10,000

Income of the person in 3rd year = Rs 3,10,000 + 10,000

⁣           ⁣         = Rs 3,20,000

Thus , Income received every year is 300000 , 310000 , 320000

This is an A.P as difference between consecutive terms is constant .

Here

first term = a = 300000

common difference (d) = 310000 - 300000

⁣           ⁣         =10000

To find the total amount received in 20 years ,

we use the formula

$S_{n} = \frac{n}{2} (2a + n - 1)d)$

Where , S , = sum of n terms of A.P.

n = number of terms

a = first term

d = common difference

Here ,

$S_n$ = Amount received in 20 years ,

n = 20 ,

a = 300000 ,

d = 10000

Putting the values

$S_{20} = \frac{20}{2} (2 \times 300000 + (20 - 1)10000)$

10 ( 600000 + 19 x 10000 ]

= 10 [ 600000 + 190000 ]

= 10 ( 790000 )

= 79,00,000

Thus , the total amount received at the end of 20 years is Rs . 79,00,000

hope it helps ☺️

Answer 2

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