Question

which of the following are the terms of an ap a)13,6,10.... b)3,6,12,24... c)28,26,24,22.... d)4,2,3,0....
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Answer 1

Answer:

Option (c)28,26,24,22....

Step-by-step explanation:

A.P(Arithmetic progression)

In all the series should have a common difference.

a)13,6,10...

Here a1 = 13; a2 = 6 and a3 = 10.

The common difference of these is:

d = a2-a1 = 13-6 = 7

     a3-a2 = 10-13 = -3

Here a2-a1 is not equal to  a3-a2.

So the given sequence is not an Arithmetic progression.

b)3,6,12,24...

Here a1 = 3; a2 = 6; a3 = 12; a4 = 24

The common difference is:

d = a2-a1 = 6-3 = 3

     a3-a2 = 12-6 = 6

Here too a2-a1 is not equal to  a3-a2.

So the given sequence is not an Arithmetic progression.

c)28,26,24,22....

Here a1 = 28; a2 = 26; a3 = 24; a4 = 22

The common difference is:

d = a2-a1 = 26-28 = -2

     a3-a2 = 24-26 = -2

Here a2-a1 is equal to  a3-a2.

So the given sequence is an Arithmetic progression.

d)4,2,3,0....

Here a1 = 4; a2 = 2; a3 = 3; a4 = 0

The common difference is:

d = a2-a1 = 2-4 = -2

     a3-a2 = 3-2 = 1

Here a2-a1 is not equal to  a3-a2.

So the given sequence is not an Arithmetic progression.