Q. 7 A

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 :

Salary for the 1st year = Rs. 8000

and according to the question,

There is an annual increment of Rs. 500

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

Now, again there is an increment of Rs. 500

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

Therefore, the series is

8000 , 8500 , 9000 , …

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

Difference between 3rd term and 2nd 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.

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