**5. A village has 4000 literate 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 ?**

**Sol. Since the no. of literate people increases by 400 every year, the population of literate people every year forms an A.P.**

**No. of people in the year 2010 (a) = 4000**

**Increase in population every year (d) = 400**

**No. of years from 2010-2020 (n) = 10**

**tn = a + (n – 1) d**

**∴**

**t10 = 4000 + (10 – 1) 400**

**∴**

**t10 = 4000 + 9 (400)**

**∴**

**t10 = 4000 + 3600**

**∴**

**t10 = 7600**

**∴**

**There will be 7600 literate people till the year 2020**

**tn = a + (n – 1) d**

**∴**

**tn = 4000 + (n – 1) 400**

**∴**

**tn = 4000 + 400n – 400**

**∴**

**tn = 3600 + 400n**

**There will be (3600 + 400n) literate people after n years.**