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

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

Question:

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. √3, √6, √9, √12, . . .

Given:

The sequence is √3, √6, √9, √12, . . .

To Find:

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

Formula:

In an Arithmetic Progression (AP), the difference between consecutive terms is constant. This constant difference is called the common difference (d).

Solution:

Let's check if the difference between consecutive terms is constant:

√6 - √3 ≈ 1.464

√9 - √6 ≈ 0.816

√12 - √9 ≈ 0.667

Since the difference between consecutive terms is not constant, the given sequence is not an AP.

Result:

The sequence √3, √6, √9, √12, . . . is not an arithmetic progression.

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