The series has an increasing difference of 6, 8, 10, 12, 14 and 16.

(a): The difference between the terms are prime numbers i.e. 2, 3, 5, 7, 11 and 13.

(c): The difference between the terms are of the form (8 * 1) (8 * 2) (8 * 4) (8 * 8) (8 * 16) .

(d): 6, 19, 60, 189, ?, 1863 6 * 3 + 1 594 * 3 + 81 19 * 3 + 3 60 * 3 + 9 189 * 3 + 27

d): The terms of series are (10 * 11) (12 * 13) (14 * 15) (16 * 17) (18 * 19) or 110 + 46 -> 156 + 54 -> 21 62 -> 272 + 70 342.

6. (b): The terms of series are dates with a common difference of 28 days. The date has been written i format dd/mm/yy.

c): The terms of the series are 1 ^ 3 - 1 2 ^ 3 + 2 3 ^ 3 - 1 4 ^ 3 + 4 5 ^ 3 - 5 6 ^ 3 + 6 .

(d): 2nd term is 2 times the 1 ^ (st) term plus 1, 3 ^ (rd) term 2 times the 2nd term minus 1, 4 ^ (th) term is 2 times the 3rd term plus 1, and so on.

9. a): 2nd term is 2 times the 1 ^ (st) term, 3 ^ (rd) term is 1 times the 2 ^ (nd) term, 4 ^ (th) term is 2 times the 3 ^ (rd) term an so on.

a): 3147+3143461; 3461+346-3807; 3807 +380 4187; 4187+418=4605; 4605 + 460 = 5065.

(d): Alternate terms of this form a series. The serie made of odd placed terms have a difference of 3, 7, 11, 13 between the terms. While the series mac of even placed terms have a difference of 5, 7, 11, 1 between the terms.

12. (b): The difference between the terms is 8, 15, 17; 15, 17

d): 4183+2054388; 4388-103 = 4285; 4285 + 205 = 4490; 4490 - 103 = boxed 4387 4387+205 = 4592.

14. (c): 132 * 3 = 396 396-4=392; 392 * 3 = 1176 117641172; 1172 * 3 = 3516 3516 - 4 = 3512

(d): The terms are 1 ^ 2 + 2 2 ^ 2 + 3 3 ^ 2 + 5 4 ^ 2 + 7 5 ^ 2 + 11 , 6 ^ 2 + 13

d): Starting from the 3rd term, each term is sum of all previous terms.

(d): The terms are 1 ^ 2 - 1 2 ^ 3 + 2 3 ^ 2 - 3 4 ^ 3 + 4 5 ^ 2 - 5 and next term will be 6 ^ 3 + 6

(a): For numerators: 2 * 1 + 2 = 4 4 * 2 + 3 = 11 11 * 3 + 4 = 37 37 * 4 + 5 = 153 For denominators: 3 * 2 + 2 = 8 8 * 2 + 2 = 18 18 * 2 + 2 = 38 38 * 2 + 2 = 78

(b): The terms are 2 * 9 , 3 * 10 5 * 11 7 * 12 and next term will be 11 * 13

(d): The difference between the consecutive terms is 2, 4, 8, 16, 32 and so on. Also alternative terms are negative.