How to prove the common difference can be a positive or negative value. What is is an arithmetic sequence (or an AP) with a common difference. Explain the difference between each consecutive term. Important Arithmetic Progression Solutions for Class 10 Maths.
Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. a, 2a, 3a, 4a, . . .
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a, 2a, 3a, 4a, . . .
a₂ – a₁ = 2a – a = a
a₃ – a₂ = 3a – 2a = a
a₄ – a₃ = 4a – 3a = a
The difference between the successive terms are same Hence, it is an A.P.
Common difference = a, next three terms of this AP is as follows:
Fifth term a₅ = a₄ + d = 4a + a = 5a
Sixth term a₆ = a₅ + d = 5a + a = 6a
Seventh term a₇ = a₆ + d = 6a + a = 7a