Hard Fun Math Patterns: Who can solve these three math patterns?

Question

2 , 2 , 4 , 6, 10, 16 ____ , _____, _____

1, 2, 4, 7, 12, 19, ____, ____, ______

2, 4, 9, 16, 25, _____, _____, _______

You need to explain exactly how you did it, so that I know you didn't get it off of some website. Whoever solves all three and explains them get the 10 points. Good Luck,some of these are hard and easy.

Answer 1

Well for first one from the third term onwards the number is equal to the sum of the previous two numbers. Therefore the remaining three numbers are 10 + 16 = 26, 16 + 26 = 42 and 26 + 42 = 68.

In third one the numbers are just the square of natural numbers except for the first one. Thus the remaining three numbers are 36, 49, 64.            

I am unable to solve the second one. I think it should be 20 in place of 19. Then the terms are one more then the sum of the previous two terms.  

Answer 2

l.  26, 42, 68                        

2.  28, 40, 56

3.  36, 49, 64

Answer 3

26,42,68

30,43,60

36,49,64

Answer 4

The first one adds the preceding two numbers together to get the next one in the sequence. 2+2=4, 2+4=6, 4+6=10, etc.

The next numbers in the sequence are 26, 32, & 58.

The second one has basically the same idea, but it is the sum of the preceding two numbers & 1. 1+2+1=4, 4+2+1=7, etc.

The next numbers in the sequence are 32, 52, & 85.

I would say squaring for the last one, but 2 is not a perfect square.

Answer 5

the first one is each number before it adds with the number to equal the next number.

2 + 2 = 4

2 + 4 = 6

4 + 6 = 10

6 + 10 = 16

and so on and so forth

second one goes up by a prime number each time. (1, 2, 3, 5, 7,  etc)

the 3rd one, theyre all square roots

Answer 6

1st one. Each new term is the sum of the previous 2

2nd one. 4 = 2 + 2

             7 = 4 + 3

             12 = 7 + 5

             19 = 12 + 7

Looks like it might be adding the next prime number to the previous term.  If so then  it would be 19 + 11 = 30

                                          30 + 13 = 43

                                          43 + 17 = 60

3rd one looks like squares  2x2, 3x3, 4x4, 5x5 so the next

terms would be 6x6 = 36, 7x7 = 49, 8x8 = 64