Which of the following is/are an Arithmetic Progression (A.P.) ?

(i) 1, 4, 9, 16, ……..

(ii) $\sqrt{3}, 2\sqrt{3}, 3\sqrt{3}, 4\sqrt{3},$ …………

(iii) 8, 6, 4, 2, ………..

1. only (i)

2. only (ii)

3. only (ii) and (iii)

4. all (i), (ii) and (iii)

In first series :

1, 4, 9, 16, ………..

16 - 9 = 7, 9 - 4 = 5.

Since, difference between consecutive terms are not equal.

∴ It is not an A.P.

In second series :

$\sqrt{3}, 2\sqrt{3}, 3\sqrt{3}, 4\sqrt{3},$ …………

$4\sqrt{3} - 3\sqrt{3} = 3\sqrt{3} - 2\sqrt{3} = 2\sqrt{3} - \sqrt{3} = \sqrt{3}$.

Since, difference between consecutive terms are equal.

∴ It is an A.P.

In third series :

8, 6, 4, 2, ……….

2 - 4 = 4 - 6 = 6 - 8 = -2.

Since, difference between consecutive terms are equal.

∴ It is an A.P.

Hence, Option 3 is the correct option.