10 class math airthmatic progessions excerise 5.1

Excerise no 5.1

1) In which of the following situations, does the list of number involved makes as airthmatic progessions and why ?

 

A) the taxi fare after each km when the fare is RS 15 for the first km and RS 8 for each additional km 

Answer 

 

It can be observed that 

Taxi fare for 1st km = 15  

Taxi fare for first 2nd km = 15+8 = 23

taki fare for first 3rd km  = 23+8 = 31

Taki fare for first 4 km    =31+8 = 39

Clearly 15, 23, 31, 39 form an A.P. because every term is 8 more than preceding term.

B) the amount of air present in the cylinder when a vaccum pump remove 1/4 À of the air remaining in the cylinder at a time

Answer 

Let the initial volume of air in a cylinder by V litres . In each stock the vaccum pump remove À 1/4 À of air remaining in the cylinder at a time . In other words after every Stoke only 1- 1/4 = 3/4 Part of air will remain

Therefore volume will be V, 3V/4 , (3V/4 )², (3V/4 )³....

Clearly it can be observed that the adjacent terms of this series do not have the same difference between them . Therefore this is not an A.P.

C) The cost of digging a well after every metre of digging when it costs RS 150 for the first metre and rises by RS 50 for each subsequent metre.

Answer

 

Cost of digging for first metre. = 150

Cost of digging for first 2 metre = 150+50 = 250

Cost of digging for first 3 metre = 200+50 250

Cost of digging for first 4 metre = 250+50 = 300

Clearly 150, 200, 250, 300 forms am A.P. because every term is 50 more than the preceding term