NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 1(ii)
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 1 (ii)
Question:
In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?
The amount of air present in a cylinder when a vacuum pump removes 1/4 of the air remaining in the cylinder at a time.
Given:
A vacuum pump removes 14 of the remaining air in a cylinder at a time.
To Find:
Whether the amounts of air remaining after each pump form an arithmetic progression.
Formula:
An arithmetic progression is a sequence where the difference between consecutive terms is constant.
Solution:
For every use the vacuum pump removes 14 x air present inside cylinder
Let the initial amount of air be A.
After the first pump, the remaining air is A - (14 A) = 34 A.
Now the air inside the cylinder is 34 A.
After the second pump, the remaining air is (34A) - (14 (34 A))
= (34 A) - ((316A))
= 12 - 316 A
= 916 A
= (34)2A.
The sequence is A, 34A, (34)2A, ... This is not an arithmetic progression since the difference between the terms are not a constant.
Result:
The amounts of air remaining do not form an arithmetic progression.
Next question solution:
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 1 (iii).
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