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

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

Question:

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. -1/2, -1/2, -1/2, -1/2, ...

Given:

The sequence: -1/2, -1/2, -1/2, -1/2, ...

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) is given by: d = an+1 - an, where an+1 and an are consecutive terms.

Solution:

Let's find the difference between consecutive terms:

a2 - a1 = - 1 2 - (- 1 2 ) = 0

a3 - a2 = - 1 2 - (- 1 2 ) = 0

Since the difference between consecutive terms is constant (0), the sequence is an AP with a common difference d = 0.

The next three terms are -1/2, -1/2, -1/2.

Result:

The sequence is an AP with common difference d = 0. The next three terms are -1/2, -1/2, -1/2.

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