(i) 9, 15, 21, 27, …
Here, 15 – 9 = 21 – 15 = 27 – 21 = 6 (which is constant)
Common difference is 6
Or d = 6
Next term = 27 + d = 27 + 6 = 33
(ii) 11, 6, 1, -4, …
Here, 6 – 11 = 1 – 6 = -5 -4 – 1 = -5 (which is constant)
d (common difference) = -5
Next term = -4 – 5 = -9
(iii) -1, -5 /6 , -2 /3 , -1 /2 , …………
-5/6 – (-1) = 1/6 and
-2/3 – (-5/6) = 1/6
d (common difference) = 1/6
Next term = -1/2 + 1/6 = -1/3
(iv) √2, √8, √18, √32, ……..
√8 – √2 = 2√2 – √2 = √2
√32 – √18 = 4√2 – 3√2 = √2
d (common difference) = √2
Next term = √32 + √2 = 4√2 + √2 = 5√2 = √50
(v) √20, √45, √80, √125, ……
√20, √45, √80, √125, ……
√45 – √20 = 3√5 – 2√5 = √5
√125 – √80 = 5√5 – 4√5 = √5
d (common difference) = √5
Next term = √125 + √5 = 5√5 + √5 = 6√5 or √180
