(i) 2, 4, 8, 16 … It can be observed that
= 4 - 2 = 2
= 8 - 4 = 4
= 16 - 8 = 8
i.e., - is not the same every time.
Therefore, the given numbers are not forming an A.P.
(ii) 2,
It can be observed that
=
i.e., is same every time.
Therefore, d = and the given numbers are in A.P.
Three more terms are
(iii) - 1.2, - 3.2, - 5.2, - 7.2 …
It can be observed that
= ( - 3.2) - ( - 1.2) = - 2
= ( - 5.2) - ( - 3.2) = - 2
= ( - 7.2) - ( - 5.2) = - 2
i.e., is same every time.
Therefore, d = - 2 The given numbers are in A.P. Three more terms are
= - 7.2 - 2 = - 9.2
= - 9.2 - 2 = - 11.2
= - 11.2 - 2 = - 13.2
(iv) - 10, - 6, - 2, 2 …
It can be observed that
= ( - 6) - ( - 10) = 4
= ( - 2) - ( - 6) = 4
= (2) - ( - 2) = 4 i.e., is same every time.
Therefore, d = 4 The given numbers are in A.P.
Three more terms are
= 2 + 4 = 6
= 6 + 4 = 10
= 10 + 4 = 14
(v) 3, , .....
It can be observed that
=
=
=
i.e., is same every time. Therefore, d =
The given numbers are in A.P.
Three more terms are
=
=
=
(vi) 0.2, 0.22, 0.222, 0.2222 ….
It can be observed that=
= 0.22 - 0.2 = 0.02
= 0.222 - 0.22 = 0.002
= 0.2222 - 0.222 = 0.0002
i.e., - is not the same every time.
Therefore, the given numbers are not in A.P.
(vii) 0, - 4, - 8, - 12 …
It can be observed that
= ( - 4) - 0 = - 4
= ( - 8) - ( - 4) = - 4
= ( - 12) - ( - 8) = - 4
i.e., is same every time.
Therefore, d = - 4, so the given numbers are in A.P.
Three more terms are
a+(5 - 1)d= -16,
a+(6 - 1)d= -20,
a+(7 - 1)d= -24
(viii) It is in AP, with common difference 0, therefore next three terms will also be same as previous ones, i.e., .
(ix) 9 - 3 = 3 - 1
6 ≠ 2
a3 - a2 ≠ a2 - a1
Therefore, the given numbers are not in A.P.
(x) It is in AP with common difference d = 2a - a = a and first term is a,
Next three terms are
a + (5 - 1)d = 5a,
a + (6 - 1)d = 6a,
a + (7 - 1)d = 7a
(xi) It is not in AP, as the difference is not constant.
(xii) It is in AP with common difference d = and a = ,
Next three terms are
a + (5 - 1)d =
a + (6 - 1)d =
a + (7 - 1)d =
(xiii) It is not in AP as difference is not constant.
(xiv) It is not in AP as difference is not constant.
(xv) It is in AP with common difference d = 52 - 1 = 24 and a = 1
Next three terms are
a + (5 - 1)d = 97,
a + (6 - 1)d = 121,
a + (7 - 1)d =145