CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?
(i)The amount of air present in a cylinder when a vacuum pump removes (14)th of the air remaining in the cylinder at a time.
(ii)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.

Open in App
Solution

(i) Let amount of air initially present in a cylinder = V

Amount of air left after pumping out air by vacuum pump = V − V4= 34 V

Amount of air left when vacuum pump again pumps out air

= 34V − [14 × 34V] = 34V−316V = 916V

So, the sequence we get is like V, 34V, 916V....

Checking for difference between consecutive terms.

34V−V = −V4

916V−34V= −3V16

Difference between consecutive terms is not constant. Therefore, it is not an arithmetic progression.

(ii)

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)


flag
Suggest Corrections
thumbs-up
2
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Simple pendulum
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon