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)

Suggest Corrections
2
Join BYJU'S Learning Program
Related Videos
Simple pendulum
PHYSICS
Watch in App
Explore more
Join BYJU'S Learning Program