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

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

Question:

In which of the following situations, does the list of numbers involved make an arithmetic progression, and why? 

The taxi fare after each km when the fare is Rs 15 for the first km and Rs 8 for each additional km.

Given:

Taxi fare for the first km = Rs 15
Taxi fare for each additional km = Rs 8

To Find:

Whether the taxi fare after each km forms an arithmetic progression.

Formula:

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

Solution:

Fare after 1 km = Rs 15

Fare after 2 km = Rs 15 + Rs 8 = Rs 23

Fare after 3 km = Rs 23 + Rs 8 = Rs 31

The sequence is 15, 23, 31, ...

Difference between consecutive terms: 23 - 15 = 8; 31 - 23 = 8

Since the difference between consecutive terms is constant (8), the sequence forms an arithmetic progression.

Result:

Yes, the taxi fare after each km forms an arithmetic progression with a common difference of 8.

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