Divya deposited Rs 1000 at compound interest at the rate of 10% per annum. The amounts at the end of first year, second year, third year, ..., form an AP. Justify your answer
Solution:
An arithmetic progression (AP) is a sequence where the two consecutive terms have the same common difference. It is obtained by adding the same fixed number to its previous term.
From the question, we have,
Amount at the end of the 1st year = Rs 1100.
Amount at the end of the 2nd year = Rs 1210.
Amount at the end of 3rd year = Rs 1331 and so on.
So, the amount at the end of 1st year, 2nd year, 3rd year, ... are 1100, 1210, 1331, …
The common difference can be found by,
a₂ - a₁ = 110
a₃ - a₂ = 121.
Since, a₂ - a₁ ≠ a₃ - a₂ ,
The above statement does not form an AP.
Therefore, it does not form an AP.
✦ Try This: A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.2 Sample Problem 2
Divya deposited Rs 1000 at compound interest at the rate of 10% per annum. The amounts at the end of first year, second year, third year, ..., form an AP. Justify your answer
Summary:
Divya deposited Rs 1000 at compound interest at the rate of 10% per annum. The amounts at the end of first year, second year, third year, ...,does not form an AP
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