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?

Solution:

Given,

The income of Subba Rao increases every year by Rs.200 and hence, it forms an AP.

Therefore, after 1995, the salaries for each year are;

5000, 5200, 5400, …

Here, first term, a = 5000

and common difference, d = 200

Let after n^th year, his salary be Rs 7000.

Therefore, by the nth-term formula of AP,

a_n = a + (n − 1) d

7000 = 5000 + (n − 1)200

200(n − 1)= 2000

(n − 1) = 10

n = 11

Therefore, in the 11th year, his salary will be Rs 7000.