NCERT Class X Chapter 5: Arithmetic Progression Example 2 (iv)
NCERT Class X Chapter 5: Arithmetic Progression Example 2(iv)
Question:
Which of the following list of numbers form an AP? If they form an AP, write the next two terms 1, 1, 1, 2, 2, 2, 3, 3, 3, . . .
Given:
The sequence: 1, 1, 1, 2, 2, 2, 3, 3, 3, . . .
To Find:
Whether the given sequence forms an arithmetic progression (AP). If it does, find the next two terms.
Formula:
In an AP, the difference between consecutive terms is constant (common difference).
Solution:
Let the given list of numbers be a1, a2, a3, a4, ...
Then,
a1 = 1
a2 = 1
a3 = 1
a4 = 2
a5 = 2
a6 = 2
a7 = 3
a8 = 3
a9 = 3
Lets calculate the common difference,
d = a2 - a1 = 1 - 1 = 0
d = a3 - a2 = 1 - 1 = 0
d = a4 - a3 = 2 - 1 = 1
The common difference changes and hence it is not a constant.
Hence, the sequence is not an AP because the difference between consecutive terms is not constant.
Result:
The given sequence 1, 1, 1, 2, 2, 2, 3, 3, 3, . . . is not an arithmetic progression.
Next question solution:
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 1 (i).
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