Question

In the following situation, involved make an arithmetic progression? and why?

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 1

Cost of digging for first metre = 150

Cost of digging for first 2 metres = 150 + 50 = 200

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

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

Clearly, 150, 200, 250, 300 … 

Check:

a = 150

d₁ - a₂ - a₁

= 200 - 150

= 50

d₂ = a₃ - a₂

= 250 - 200

= 50

d₃ = a₄ - a₃

= 300 - 250

= 50

Common difference = 50

Here the common difference is the same hence this series is A.P.