Which of the following sequence are in A.P. ?

(a) 3, 7, 11, 15, …….

(b) 8, 4, 2, 1, ……..

(c) 1, −1, −3, −5, …….

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Solution

(a) 3, 7, 11, 15 …

It can be observed that:

Thus, the difference between a term and its preceding term is constant.

Thus, the given sequence is in A.P.

(b) 8, 4, 2, 1 …

It can be observed that:

Thus, the difference between a term and its preceding term varies.

Thus, the given sequence is not in A.P.

(c)

It can be observed that:

Thus, the difference between a term and its preceding term is constant.

Thus, the given sequence is in A.P.

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