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

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

Question:

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. – 10, – 6, – 2, 2, . . .

Given:

The sequence: –10, –6, –2, 2, . . .

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 common difference (d) is given by: d = an - an-1, where an is the nth term and an-1 is the (n-1)th term.

Solution:

Let's find the differences between consecutive terms:

–6 – (–10) = 4

–2 – (–6) = 4

2 – (–2) = 4

Since the difference between consecutive terms is constant (4), the sequence is an arithmetic progression (AP).

The common difference, d = 4.

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

2 + 4 = 6

6 + 4 = 10

10 + 4 = 14

Result:

The sequence is an AP with a common difference d = 4. The next three terms are 6, 10, and 14.

© Kaliyuga Ekalavya. All rights reserved.

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