√3 , 2 √3 , 3 √3 ,... verify that the following is an AP, and then write its next three terms

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 above, we have,

a₁ = √3

a₂ = 2 √3

a₃ = 3 √3

Calculating the difference, we get,

a₂ - a₁ = 2 √3 - √3 = √3

a₃ - a₂ = 3 √3 - 2 √3 = √3

So, a₂ - a₁ = a₃ - a₂

Each successive term of the given list has the same difference.

Therefore, it forms an AP.

The next three terms are,

a₄ = a + 3d = √3 + 3 (√3) = 4√3

a₅ = a + 4d = √3 + 4(√3) = 5√3

a₆ = a + 5d = √3 + 5(√3) = 6√3

Therefore, it forms an AP and the next three terms are 4√3, 5√3 and 6√3.

✦ Try This: The n^th term of an A. P. is 6n + 11. Find the common difference

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

NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 2 (iii)

√3 , 2 √3 , 3 √3 ,... verify that the following is an AP, and then write its next three terms

Summary:

√3 , 2 √3 , 3 √3 ,... forms an A.P and the next 3 terms are 4√3,5√3,6√3.

☛ Related Questions:

• The sum of the first three terms of an AP is 33. If the product of the first and the third term exce . . . .
• Match the APs given in column A with suitable common differences given in column B
• 0, 1/4 , 1/2 , 3/4 ,... verify that the following is an AP, and then write its next three terms