a + b, (a + 1) + b, (a + 1) + (b + 1), … 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.

The nth term of an AP is

aₙ = a + (n - 1 )d.

a = first term

aₙ = nth term

d = common difference.

a₁ = a + b

a₂ = (a + 1) + b

a₃ = (a + 1) + (b + 1)

Calculating the difference, we get,

a₂ - a₁ = (a + 1) + b - (a + 1) + (b + 1) = a + 1 + b - a - b = 1.

a₃ - a₂ = (a + 1) + (b + 1) — [(a + 1) + b] = a + 1 + b + 1 - a - 1 - b = 1

Therefore, 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 + 2) + (b + 1)

a₅ = (a + 2) + (b + 2)

a₆ = (a + 3) + (b + 2)

Therefore, it forms an AP and the next three terms are (a + 2) + (b + 1), (a + 2) + (b + 2) and (a + 3) + (b + 2).

✦ Try This: If the 8^th term of an A. P. is 31 and the 15^th term is 16 more than the 11^th term, find the A. P

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

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

a + b, (a + 1) + b, (a + 1) + (b + 1), … verify that the following is an AP, and then write its next three terms

Summary:

a + b, (a + 1) + b, (a + 1) + (b + 1), …forms an A.P and the next 3 terms are (a + 2) + (b + 1),(a + 2) + (b + 2),(a + 3) + (b + 2)

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☛ 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