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

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

Question:

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 2, 5/2, 3, 7/2, . . .

Given:

The sequence is 2, 5/2, 3, 7/2, . . .

To Find:

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

Formula:

In an AP, the common difference (d) between consecutive terms is constant. d = an+1 - an, where an is the nth term.

Solution:

Let's find the differences between consecutive terms:

5/2 - 2 = 12 = 0.5

3 - 5/2 = 12 = 0.5

7/2 - 3 = 12 = 0.5

Since the difference between consecutive terms is constant (0.5 or 1/2), the sequence is an AP with a common difference d = 12.

Next three terms:

a5 = 7/2 + 1/2 = 4

a6 = 4 + 1/2 = 9/2

a7 = 9/2 + 1/2 = 5

Result:

The sequence is an AP with common difference d = 12. The next three terms are 4, 92, 5.

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