NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (xv)
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (xv)
Question:
Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 12, 52, 72, 73, . . , . . .
Given:
The sequence is 12, 52, 72, 73, . . . This translates to 1, 25, 49, 73, ...
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 arithmetic progression (AP), the difference between consecutive terms is constant. This difference is called the common difference (d). an = a1 + (n-1)d
Solution:
Let's find the difference between consecutive terms:
25 - 1 = 24
49 - 25 = 24
73 - 49 = 24
Since the difference between consecutive terms is constant (24), the sequence is an AP.
The common difference, d = 24
To find the next three terms, we add the common difference (24) repeatedly:
73 + 24 = 97
97 + 24 = 121
121 + 24 = 145
Result:
The given sequence is an AP with a common difference of 24. The next three terms are 97, 121, and 145.
Next question solution:
NCERT Class X Chapter 5: Arithmetic Progression Example 3
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