√3, √12, √27, √48… 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 = √3

t₂ = √12

t₃ = √27

t₄ = √48.

Calculating the difference, we get the value as,

t₂ - t₁ = 2√3-√3=√3

t₃ - t₂ = 3√3-2√3=√3

t₄ - t₃ = 4√3-3√3=√3.

The difference between each successive term is the same

Therefore, the given list of numbers form an AP.

✦ Try This: Which of the following forms an AP? Justify your answer.

√2,√18,√21,√48

From the question, we have,

t₁ = √2

t₂ = √18

t₃ = √21

t₄ = √48.

Calculating the difference, we get the value as,

t₂ - t₁ = √18 - √2 = 3√2 - √2 = 2√2

t₃ - t₂ = √21 - √18

t₄ - t₃ = √48 - √21

The difference between each successive term is not the same

Therefore, the given list of numbers does not form an AP.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

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NCERT Exemplar Class 10 Maths Exercise 5.2 Problem 1 (vii)

√3, √12, √27, √48… 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 √3,√12,√27,√48 form an AP

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☛ Related Questions:

• Justify whether it is true to say that -1, -3 /2 , -2, 5/2 ,... forms an AP as a₂ - a₁ = a₃ - a₂
• For the AP: -3, -7, -11, ..., can we find directly a₃₀ - a₂₀ without actually finding a₃₀ and a₂₀? G . . . .
• Two APs have the same common difference. The first term of one AP is 2 and that of the other is 7. T . . . .