Answer 1:

2+3^0=3

3+3^ 1=6

6+3^2= 15

15+3^3=42

42+3^4= 123

So: 2,3,6, (15)(42)

Law: an = a (n- 1)+3 (n- 1)

Each number is equal to its previous number plus the n- 1 power of 3.

Answer 2:

2X3=6

3X6= 18

6X 18= 108

So the answer is: 2,3,6, (18)( 108).

Law: Every number is equal to the product of the first two numbers.

Answer 3:

2X 1.5=3

3X( 1.5+0.5)=6

6X(2+0.5)= 15

15X(2.5+0.5)=45

So: 2,3,6, (15)(45)

Each number is equal to the previous number, multiplied by a coefficient, and each time added by 0.5.

Answer 4:

2+ 1=3

3+3=6

6+5= 1 1

1 1+7= 18

So: 2,3,6, (1 1)( 18)

Law: Every number is equal to the last number, plus addend and 2.

Answer 5:

2+ 1=3

3+ 1+2=6

6+ 1+2+3= 12

12+ 1+2+3+4=22

22+ 1+2+3+4+5=37

So: 2,3,6, (12)(22)

Law: Each term is equal to the previous number plus a natural number.