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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.
Solution
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.
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