Answer :

(i)


Common difference, d1 = 6 – 3 = 3


Common difference, d2= 12 – 6 = 6


Since, d1 ≠ d2


Therefore, it’s not an A.P.


(ii)


Common difference, d1 = -4 – 0 = -4


Common difference, d2= -8 – (-4) = - 4


Since, d1 = d2


Therefore, it’s an A.P. with common difference, d = -4


(iii)


Common difference, d1= - =


Common difference, d2 = - =


Since, d1 ≠ d2


Therefore, it’s not an A.P.


(iv)


Common difference, d1= 2 – 12 = -10


Common difference, d2= -8 -2 = -10


Since,d1 = d2


Therefore, it’s an A.P. with common difference, d = -10


(v)


Common difference, d1= 3 – 3 = 0


Common difference, d2= 3 – 3 = 0


Since, d1=d2


Therefore, it’s an A.P. with common difference, d = 0


(vi)


Common difference, d1= p + 90 – p = 90


Common difference, d2= p + 180 – p – 90 = 90


Since, d1=d2


Therefore, it’s an A.P. with common difference, d = 90


(vii)


Common difference, d1= 1.7 – 1.0 = 0.7


Common difference, d2= 2.4 – 1.7 = 0.7


Since, d1=d2


Therefore, it’s an A.P. with common difference, d = 0.7


(viii)


Common difference, d1= -425 + 225 = -200


Common difference, d2= -625 + 425 = -200


Since, d1=d2


Therefore, it’s an A.P. with common difference, d = -200


(ix)


Common difference, d1= 10 + 26 – 10 = 26 = 64


Common difference, d2 = 10 + 27 – 10 – 26 = 26 (2 – 1) = 64


Since, d1=d2


Therefore, it’s an A.P. with common difference, d = 64


(x)


Common difference, d1 = (a + 1) + b – a – b = 1


Common difference, d2 = (a + 1) + (b + 1) – (a + 1) – b = 1


Since, d1 = d2


Therefore, it’s an A.P. with common difference, d = 1


(xi)


Common difference, d1= 32 – 12 = 8


Common difference, d2 = 52 – 32 = 25 – 9 = 16


Since, d1≠d2


Therefore, it’s not an A.P.


(xii)


Common difference, d1 = 52 – 12 = 24


Common difference, d2 = 72 – 52 = 24


Since, d1 = d2


Therefore, it’s an A.P. with common difference, d = 24


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