Question

Subba Rao started work in 1995 at an annual salary of ₹ 5000 and received an increment of ₹ 200 each year. In which year did his income reach ₹ 7000?

Answer 1

It can be observed that the incomes that Subba Rao obtained in various years are in A.P as every year, his salary is increased by ₹ 200.
Therefore, the salaries of each year after 1995 are :
5000, 5200, 5400, …
Here, a = 5000
d = 200
Let after n year, his salary be ₹ 7000.
The $n^{th}$ term of an A.P is given by ,
$a_n=a+(n-1)d$

So, 7000 = 5000 + (n − 1) 200
200(n − 1) = 2000
(n − 1) = 10
n = 11
Thus, 1995 + 11 = 2006
Hence, his salary reached ₹ 7000 in the year 2006.