NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (x)
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (x)
Question:
Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. a, 2a, 3a, 4a, . . .
Given:
The sequence: a, 2a, 3a, 4a, . . .
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 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 difference between consecutive terms:
2a - a = a
3a - 2a = a
4a - 3a = a
Since the difference between consecutive terms is constant and equal to 'a', the given sequence is an arithmetic progression (AP).
The common difference is d = a.
To find the next three terms, we add the common difference to the last term repeatedly:
5th term = 4a + a = 5a
6th term = 5a + a = 6a
7th term = 6a + a = 7a
Result:
Yes, the given sequence is an AP with a common difference of a. The next three terms are 5a, 6a, and 7a.
Next question solution:
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (xi).
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