1(v)
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, ...........
- (a)only (i)
- (b)only (ii)
- (c)only (ii) and (iii)
- (d)all (i), (ii) and (iii)
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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.