NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (ii)
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (ii)
Question:
Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 2, 5/2, 3, 7/2, . . .
Given:
The sequence is 2, 5/2, 3, 7/2, . . .
To Find:
Whether the given sequence is an Arithmetic Progression (AP). If it is an AP, find the common difference (d) and the next three terms.
Formula:
In an AP, the common difference (d) between consecutive terms is constant. d = an+1 - an, where an is the nth term.
Solution:
Let's find the differences between consecutive terms:
5/2 - 2 = 12 = 0.5
3 - 5/2 = 12 = 0.5
7/2 - 3 = 12 = 0.5
Since the difference between consecutive terms is constant (0.5 or 1/2), the sequence is an AP with a common difference d = 12.
Next three terms:
a5 = 7/2 + 1/2 = 4
a6 = 4 + 1/2 = 9/2
a7 = 9/2 + 1/2 = 5
Result:
The sequence is an AP with common difference d = 12. The next three terms are 4, 92, 5.
Next question solution:
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (iii).
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