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

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

Question:

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 1, 3, 9, 27, . . .

Given:

The sequence: 1, 3, 9, 27, . . .

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 difference between consecutive terms is constant. This constant difference is called the common difference (d).

Solution:

Let's check if the given sequence is an AP by finding the difference between consecutive terms:

3 - 1 = 2

9 - 3 = 6

27 - 9 = 18

Since the differences between consecutive terms are not constant (2, 6, 18), the given sequence is not an arithmetic progression (AP).

Result:

The given sequence 1, 3, 9, 27, . . . is not an AP.

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