CBSE NCERT Solutions Chapter 5 Arithmetic Progressions Exercise 5.1 Question 1
1. 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 Rs 15 for the first km and Rs 8 for each additional km.
Taxi fare for 1st km = Rs 15
Taxi fare after 2 km = 15+8 = Rs 23
Taxi fare after 3 km = 23+8 = Rs 31
Taxi fare after 4 km = 31 +8 = Rs 39
Therefore, the sequence is 15, 23, 31, 39 .....
It is an arithmetic progression because difference between any two consecutive terms is constant which is 8.
(23-15=8, 31-23= 8, 39-31=8,....)
(ii) The amount of air present in a cylinder when a vacuum pump removes of the air remaining in the cylinder at a time.
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 constant. Therefore, it is not an arithmetic progression.
(iii) The cost of digging a well after every meter of digging, when it costs Rs 150 for the first meter and rises by Rs 50 for each subsequent meter.
Cost of digging 1 meter of well = Rs 150
Cost of digging 2 meters of well = 150+50= Rs 200
Cost of digging 3 meters of well = 200+50 = Rs 250
Therefore, we get a sequence of the form 150, 200, 250 ....
It is an arithmetic progression because difference between any two consecutive terms is constant.
(200-150 = 250-200 = 50,...)
Here, difference between any two consecutive terms which is also called common difference is equal to 50.
(iv) The amount of money in the account every year, when Rs 10,000 is deposited at compound Interest at 8% per annum.
Amount in bank after Ist year = (1)
Amount in bank after two years = (2)
Amount in bank after three years = (3)
Amount in bank after four years = (4)
It is not an arithmetic progression because
(Difference between consecutive terms is not constant)
Therefore, it is not an Arithmetic Progression.