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

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

Question:

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. a, a2, a3, a4

Given:

Sequence: a, a2, a3, a4, ...

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

Solution:

Let's examine the differences between consecutive terms:

a2 - a = a(a - 1)

a3 - a2 = a2(a - 1)

Since a2(a - 1) ≠ a(a - 1) unless a = 1 or a = 0, the difference between consecutive terms is not constant.

Therefore, the given sequence is not an Arithmetic Progression.

Result:

The sequence a, a2, a3, a4, ... is not an AP.

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