2, 2² , 2³ , 2⁴, ... 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 = 2
t₂ = 4
t₃ = 8
t₄ = 16
Calculating the difference, we get the value as,
t₂ - t₁ = 4 - 2 = 2
t₃ - t₂ = 8 - 4 = 4
t₄ - t₃ = 16 - 8 = 8
The difference of each successive term is not the same.
Therefore, it does not form an A.P.
✦ Try This: Which of the following forms an AP? Justify your answer
3, 3² , 3³ , 3⁴, ...
From the question, we have,
t₁ = 3
t₂ = 3²
t₃ = 3³
t₄ = 3⁴
Calculating the difference, we get the value as,
t₂ - t₁ = 9 - 3 = 6
t₃ - t₂ = 27 - 9 = 18
t₄ - t₃ = 81 - 27 = 54
The difference of each successive term 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 (vi)
2, 2² , 2³ , 2⁴ ... form an AP? Justify your answer
Summary:
An arithmetic progression (AP) is a sequence where the two consecutive terms have the same common difference. A given list of numbers 2, 2² , 2³ , 2⁴4, ... does not form an AP
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