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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Similar questions

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

(a) 3, 7, 11, 15, …….

(b) 8, 4, 2, 1, ……..

\frac{1}{\sqrt{(b)} + \sqrt{(c)}}, \frac{1}{\sqrt{(c)} + \sqrt{(a)}}, \frac{1}{\sqrt{(a)} + \sqrt{(b)}}

a, b, c

\frac{1}{b c}, \frac{1}{a c}, \frac{1}{a b}

a b c

If $a (\frac{1}{b} + \frac{1}{c}), b (\frac{1}{c} + \frac{1}{a}) c (\frac{1}{a} + \frac{1}{b})$ are in A.P., prove that a, b, c are in A.P.

a (\frac{1}{b} + \frac{1}{c}), b (\frac{1}{c} + \frac{1}{a}), c (\frac{1}{a} + \frac{1}{b})

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