CBSE Class 10-Mathematics: Chapter – 5 Arithmetic Progressions Part 24 (For CBSE, ICSE, IAS, NET, NRA 2023)
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Question 23:
In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?
(i) The taxi fare after each km when the fare is ₹ for the first km and ₹ for each additional km.
(ii) The amount of air present in a cylinder when a vacuum pump removes 14th of the air remaining in the cylinder at a time.
(iii) The cost of digging a well after every meter of digging, when it costs ₹ 150 for the first meter and rises by ₹ 50 for each subsequent meter.
(iv) The amount of money in the account every year, when ₹ 10,000 is deposited at compound Interest at per annum
Answer:
(i) Taxi fare for 1st , Taxi fare after
Taxi fare after
Taxi fare after
Therefore, the sequence is
It is an arithmetic progression because difference between any two consecutive terms is equal which is .
(ii) Let amount of air initially present in a cylinder
Amount of air left after pumping out air by vacuum pump
Amount of air left when vacuum pump again pumps out air
So, the sequence we get is like
Checking for difference between consecutive terms …
Difference between consecutive terms is not equal.
Therefore, it is not an arithmetic progression.
(iii) Cost of digging 1 meter of well
Cost of digging 2 meters of well
Cost of digging 3 meters of well
Therefore, we get a sequence of the form
It is an arithmetic progression because difference between any two consecutive terms is equal.
Here, difference between any two consecutive terms which is also called common difference is equal to .
(iv) Amount in bank after year
Amount in bank after two years
Amount in bank after three years
Amount in bank after four years
It is not an arithmetic progression because
(Difference between consecutive terms is not equal)
Therefore, it is not an Arithmetic Progression.