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

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

Question:

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. – 1.2, – 3.2, – 5.2, – 7.2, . . .

Given:

The sequence: – 1.2, – 3.2, – 5.2, – 7.2, . . .

To Find:

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

Formula:

In an AP, the common difference (d) is given by: d = an - an-1, where an and an-1 are consecutive terms.

Solution:

Let's find the difference between consecutive terms:

– 3.2 – (– 1.2) = –3.2 + 1.2 = –2

– 5.2 – (– 3.2) = –5.2 + 3.2 = –2

– 7.2 – (– 5.2) = –7.2 + 5.2 = –2

Since the difference between consecutive terms is constant and equal to –2, the given sequence is an arithmetic progression (AP).

The common difference, d = –2

To find the next three terms, we add the common difference successively:

– 7.2 + (–2) = –9.2

– 9.2 + (–2) = –11.2

– 11.2 + (–2) = –13.2

Result:

The given sequence is an AP with a common difference of –2. The next three terms are –9.2, –11.2, and –13.2.

© Kaliyuga Ekalavya. All rights reserved.

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