Question 1(v)Which of the following is/are an Arithmetic Progression (A.P.) ?(i) 1, 4, 9, 16, ........(ii) 3,23,33,43,\sqrt{3}, 2\sqrt{3}, 3\sqrt{3}, 4\sqrt{3},3,23,33,43, ............(iii) 8, 6, 4, 2, ...........only (i)only (ii)only (ii) and (iii)all (i), (ii) and (iii)

Question

Question 1(v)Which of the following is/are an Arithmetic Progression (A.P.) ?(i) 1, 4, 9, 16, ........(ii) 3,23,33,43,\sqrt{3}, 2\sqrt{3}, 3\sqrt{3}, 4\sqrt{3},3​,23​,33​,43​, ............(iii) 8, 6, 4, 2, ...........only (i)only (ii)only (ii) and (iii)all (i), (ii) and (iii)

Accepted Answer

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 :3,23,33,43,\sqrt{3}, 2\sqrt{3}, 3\sqrt{3}, 4\sqrt{3},3​,23​,33​,43​, ............43−33=33−23=23−3=34\sqrt{3} - 3\sqrt{3} = 3\sqrt{3} - 2\sqrt{3} = 2\sqrt{3} - \sqrt{3} = \sqrt{3}43​−33​=33​−23​=23​−3​=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.

Solved 2024 Specimen Paper ICSE Class 10 Mathematics — Question 5

Question 1(v)