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Question

A village has 4000 literate people people in the year 2010 and this number increases by 400 per year. How many literate people will be there till the year 2020? Find a formula to know the number of literate people after n years?

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Solution

In 2010, the number of literate people in the village is 4000 and this number increases by 400 every year.

Thus, the numbers of literate people in the village are in an A.P., with the first term as a = 4000 and the common difference as d = 400.

To find the number of literate people in the village after n years, we need to find the n^{th} term of the A.P.

We know that the n^{th} term of an A.P. is t_{n} = a + (n – 1)d.

By taking a = 4000, d = 400 and n = n, we get:

t_{n} = 4000 + (n – 1)400

$\Rightarrow $ t_{n} = 4000 + 400n – 400

$\Rightarrow $ t_{n} = 3600 + 400n

Thus, the number of literate people in the village after n years is t_{n} = 3600 + 400n.

Now,

To find the number of literate people in the village in the year 2020, we need to put

n = 2020 – 2010 = 10 in t_{n} = 3600 + 400n.

Thus, we have:

t_{10} = 3600 + 400 × 10 = 3600 + 4000 = 7600

Thus, the number of literate people in the village in the year 2020 is 7600.

Thus, the numbers of literate people in the village are in an A.P., with the first term as a = 4000 and the common difference as d = 400.

To find the number of literate people in the village after n years, we need to find the n

We know that the n

By taking a = 4000, d = 400 and n = n, we get:

t

$\Rightarrow $ t

$\Rightarrow $ t

Thus, the number of literate people in the village after n years is t

Now,

To find the number of literate people in the village in the year 2020, we need to put

n = 2020 – 2010 = 10 in t

Thus, we have:

t

Thus, the number of literate people in the village in the year 2020 is 7600.

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