# Find out which of

(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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