How to a arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutive terms is always the same. Find the definition of an arithmetic progression, where the difference between any two consecutive terms is a constant (in this case √2). NCERT Class 10th Maths Important Arithmetic Progression, Page No:99, Exercise 5.1, Session 2022-2023.
Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 3, 3 + √2 , 3 + 2√2 , 3 + 3√2 , . . .
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3, 3 + √2 , 3 + 2√2 , 3 + 3√2 , . . .
a₂ – a₁ = 3 +√2 – 3 = √2
a₃ – a₂ = 3 + 2√2 – (3 +√2) = √2
a₄ – a₃ = 3 + 3√2 – (3 + 2√2) = √2
The difference between the successive terms are same Hence, it is an A.P.
Common difference = 4, next three terms of this AP is as follows:
Fifth term a₅ = a₄ + d = 3 + 3√2 + √2 = 3 + 4√2
Sixth term a₆ = a₅ + d = 3 +4√2 + √2 = 3 + 5√2
Seventh term a₇ = a₆ + d = 3 + 5√2 + √2 = 3 + 6√2 .