**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.**

**Solution:**

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.**

**Solution:**

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.**

**Solution:**

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.**

**Solution:**

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.**