Question

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 20 for the first km and rises by ₹ 8 for each additional km.
(ii) 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.
(iii) The cost of digging a well, after every metre of digging, when it costs 150 for
the first metre and rises by ₹ 50 for each subsequent metre.
(iv) The amount of money in the account every year, when ₹10000 is deposited at compound interest at 8 % per annum.

Answer 1

Hi ,

i ) From the given data the taxi fare

are 20 ,28 , 36 ,...

first term ( a1 ) = 20 ,

second term ( a2 ) = 28 ,

a3 = 36 ,

a2 - a1 = 28 - 20 = 8

a3 - a2 = 36 - 28 = 8

Therefore ,

The difference of fare each kilometre

is same .

So , given data is an A.P

ii ) Let the amount of air present

in a cylinder is x .

From the given data the air present

in the cylinder is x , x/4 , x/16 , x/64 ,..

first term ( a1 ) = x ,

a2 = x/4 ,

a3 = x/16 ,

a4 = x/64 ,

a2 - a1 = x/4 - x = -3x/4

a3 - a2 = x/16 - x/4 = -3x/16

Therefore ,

a2 - a1 ≠ a3 - a2

So , the given data is not in A.P

iii ) From the given data cost of

digging a well is 150 ,200 ,250 , 300,..

a1 = 150 ,

a2 = 200 ,

a3 = 250 ,

a2 - a1 = 200 - 150 = 50 ,

a3 - a2 = 250 - 200 = 50

Therefore ,

a2 - a1 = a3 - a2

So, the given data is in A.P

iv )No , it's not , as the difference of

interest I another same for the

consecutive years.

I hope this helps you.

: )

Answer 2

This pics may help you please mark me as branilest pleaseeeeeeeeeeeeeeeee