NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (xiv)

Question:

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 1², 3², 5², 7², . . .

Given:

The sequence: 1², 3², 5², 7², . . .

To Find:

Whether the given sequence is an AP. If it is, find the common difference (d) and the next three terms.

Formula:

In an Arithmetic Progression (AP), the common difference (d) between consecutive terms is constant. d = a_n+1 - a_n

Solution:

The given sequence is: 1², 3², 5², 7², ... which is 1, 9, 25, 49, ...

Let's find the differences between consecutive terms:

9 - 1 = 8

25 - 9 = 16

49 - 25 = 24

Since the differences are not constant, this is not an AP.

Result:

The given sequence is not an Arithmetic Progression (AP).

Next question solution:

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (xv).

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