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State if the following is true or false.

In following situation, the list of numbers involve arithmetic progression.

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

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True

False

answer is A.

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Detailed Solution

Given that,
The starting salary is 8000.
The increment is 500.
Now, the second year salary will be,

a 2 = 8000 + 500 ⇒ a 2 = 8500

Now, the salary for the third year will be,

a 3 = 8500 + 500 ⇒ a 3 = 9000

So, the series will be

8000, 8500, 9000, ...

.
Again, the common difference between two terms is,

a 2 − a 1 = 8500 − 8000 ⇒ a 2 − a 1 = 500

a 3 − a 2 = 9000 − 8500 ⇒ a 3 − a 2 = 500

Hence, salary in successive years is in A.P. with common difference of 500 and first term 8000.
The numbers form an A.P.
Therefore, the statement is true.
Hence, option 1 is correct.

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