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.

Question

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.

Answer 1

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 2^nd year = Rs. 100 +50

= Rs. 150

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

= Rs. 200

Therefore, the series is

100, 150, 200, 250,…

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

Difference in the 3^rd term and 2^nd 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