NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 1(iii)

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 1 (iii)

Question:

In which of the following situations, does the list of numbers 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.

Given:

The cost of digging the first metre of a well is Rs 150. 

The cost increases by Rs 50 for each subsequent metre.

To Find:

Whether the costs form an arithmetic progression.

Formula:

An arithmetic progression is a sequence of numbers such that the difference between any two consecutive terms is constant.

Solution:

The cost for the first metre is Rs 150.

The cost for the second metre is Rs 150 + Rs 50 = Rs 200.

The cost for the third metre is Rs 200 + Rs 50 = Rs 250.

The common difference between consecutive terms is 

200 - 150 = 50

250 - 200 = 50

Since the difference between consecutive terms is constant, the costs form an arithmetic progression.

Result:

Yes, the cost of digging form an arithmetic progression.

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