1/2, 1/3, 1/4….. form an AP? Justify your answer
Solution:
An arithmetic progression (AP) is a sequence where the two consecutive terms have the same common difference. It is obtained by adding the same fixed number to its previous term.
From the question, we have,
t₁ = 1/2
t₂ = 1/3
t₃ = 1/4.
Calculating the difference, we get the value as,
t₂ - t₁ = 1/3 - 1/2 = (2 - 3)/6 = -1/6.
t₃ - t₂ = 1/4 - 1/3 = (3 - 4)/12 = -1/12.
The difference of each successive terms is not the same,
Therefore, it does not form an A.P
✦ Try This: Which of the following forms an AP? Justify your answer.
2/3, 4/3, 5/3,.....................
From the question, we have,
t₁= 2/3
t₂ = 4/3
t₃ = 5/3.
Calculating the difference, we get the value as,
t₂ - t₁ = 4/3 - 2/3 = 2/3
t₃ - t₂ = 5/3 - 4/3 = 1/3
The difference of each successive terms is not the same,
Therefore, it does not form an A.P
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.2 Problem 1 (v)
1/2, 1/3 , 1/4….. form an AP? Justify your answer
Summary:
An arithmetic progression is a sequence where each term, except the first term, is obtained by adding a fixed number to its previous term. A given list of numbers 1/2, 1/3, 1/4 does not form an AP
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