In the year 2010 in the village there were 4000 people who were literate. Every year the number of literate people increases by 400. How many people will be literate in the year 2020?
ANSWER
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Hint: Assume 4000 as the first term of the A.P. and 400 as the common difference. Number of years from 2010 to 2020 will give you ‘n’ and use all these values in the formula ${{t}_{n}}=a+\left( n-1 \right)d$ to get the final answer.
Complete step-by-step answer: To solve the given question we will write the given data first, therefore, Number of literate people in the year 2010 = 4000 Increase in literate people every year = 400 Now, as there is a constant increment every year and we have asked the literacy in 2020 therefore we can arrange the series of literature people as follows, Number of literate people in 2010 = 4000 Number of literate people in 2011 = 4000 + 400 = 4400 Number of literate people in 2012 = 4400 + 400 = 4800 And so on……. If we observe above equations then we can conclude that every number is increasing with a constant difference and hence forms an A.P. therefore we can write the A.P. of literature people as, 4000, 4400, 4800, …………………….. Therefore, a = 4000 and d = 400 ……………………………………….. (1) As we have to find the literacy in 2020 i.e. we have to find the term which comes in 2020 we can find this as follows, Therefore number of years from 2010 to 2020 will become ‘n’ Therefore n = 2020 – 2010 = 10 …………………………………………………… (2) Therefore we have to find the 10th term of the A.P. and for that we should know the formula given below, Formula: ${{t}_{n}}=a+\left( n-1 \right)d$ By using the formula given above we can write the formula for 10th term of an A.P as follows, ${{t}_{10}}=a+(10-1)d$ By substituting the values of equation (1) and equation (2) in the above equation we will get, $\therefore {{t}_{10}}=4000+(10-1)(400)$ By simplifying the above equation we will get, $\therefore {{t}_{10}}=4000+(9)(400)$ By doing the multiplication in the above equation we will get, \[\therefore {{t}_{10}}=7600\] If we perform addition in the above equation we will get, \[\therefore {{t}_{10}}=7600\] As our 10th term is the number of literature people in 2020 therefore we can write, The number of literature people in 2020 will be equal to 7600.
Note: Many students will make the mistake of multiplying 400 by 10 and adding it in 4000 and which will result in a wrong answer i.e. 8000 therefore be aware while solving this problem. Here we are focused on finding the number of people who are literate in 2020 instead of finding the sum of the number of literate people till 2020.