How to prove the sequence is an arithmetic progression with a common difference.
How to possible to check that the difference between any two consecutive terms in the sequence is always the same.
Solve the Arithmetic progressions Questions, Class 10th maths, NCERT books EXERCISE 5.1, CBSE Board and U P board and Others state Board.
Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 0, – 4, – 8, –12, . . .
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0, – 4, – 8, –12, . . .
a₂ – a₁ = – 4 – 0 = – 4
a₃ – a₂ = – 8 – (-4) = – 4
a₄ – a₃ = – 12 – (-8) = – 4
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 = – 12 – 4 = – 16
Sixth term a₆ = a₅ + d = – 16 – 4 = – 20
Seventh term a₇ = a₆ + d = – 20 – 4 = -24.