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Question

# In which of the following situations, the sequence of numbers formed will form an A.P?(i) The cost of digging a well for the first metre is Rs.150 and rises by Rs.20 for each succeeding metre(ii) The amount of air present in the cylinder when a vacuum pump removes each time 14 of their remaining in the cylinder.

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Solution

## 1) Given, the cost of digging a well for the first meter is 150 and rises by Rs. 20.hence for first meter (n=1)the cost is given bya1=150 (i.e.,first term of A.P) and rises by Rs. 20 which is the common difference of A.P.hence d=20cost of digging nth meter is given by.an=a1+(n−1)dhence this problem is an A.P 150,170,190,210,....... because their is a constant common difference2) let initially the cylinder has amount of air a1=x then first time vacuum pump removes 14 of the remaining air in cylinder.hence remaining air is a2=x−x4=3x4 again second time vacuum pump removes 14 of the remaining air in cylinder.hence remaining air is a3=3x4−3x16=9x16 the common difference in first and second term is d=a2−a1=3x4−xd1=−x4the common difference in second and third term is d=a3−a3=9x16−3x4d2=−3x4since,d1≠d2hence their is not a constant common difference hence it is not an A.P

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