The salary of a teacher in successive years when starting salary is Rs. 8000, with an annual increment of Rs. 500.

Question

In which of the following situations does the list of numbers involved arithmetic progression, and why?

The salary of a teacher in successive years when starting salary is Rs. 8000, with an annual increment of Rs. 500.

Answer 1

Salary for the 1^st year = Rs. 8000

and according to the question,

There is an annual increment of Rs. 500

⇒ The salary for the 2^nd year = Rs. 8000 + 500 = Rs.8500

Now, again there is an increment of Rs. 500

⇒ The salary for the 3^rd year = Rs. 8500 +500 = Rs. 9000

Therefore, the series is

8000 , 8500 , 9000 , …

Difference between 2^nd term and 1^st term = 8500 – 8000 = 500

Difference between 3^rd term and 2^nd term = 9000 – 8500 = 500

Since, the difference is same.

Hence, salary in successive years are in AP with common difference d = 500 and first term a is 8000.