Q7 of 176 Page 9

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

The money saved by Sudha in successive years when she saves Rs. 100 the first year and increased the amount by Rs. 50 every year.

The money saved by Sudha in the first year = Rs. 100


According to the question,


Sudha increased the amount by Rs. 50 every year


⇒ The money saved by Sudha in a 2nd year = Rs. 100 +50


= Rs. 150


The money saved by Sudha in a 3rd year = Rs. 150 + 50


= Rs. 200


Therefore, the series is


100, 150, 200, 250,…


Difference in the 2nd term and 1st term = 150 – 100 = 50


Difference in the 3rd term and 2nd term = 200 – 150 = 50


Since the difference is the same.


Therefore, the money saved by Sudha in successive years form an AP with a = Rs 100 and d =Rs 50


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