Answers to 8/27 Puzzle

Since I posted the puzzle a day late, I gave you an extra day to work on it.

Here are the answers and explanations:

1, 4, 7, 10, 13, 16, ... 19. The numbers increase by three.

4, 3, 5, 4, 6, 5, 7, ... 6. The difference between each consecutive pair of numbers, starting with the first two, is 1: 4-3=1, 5-4=1, and so on.

2, 4, 8, 16, 32, 64, ... 128. Each number is twice the one before it.

2, 3, 5, 7, 11, 13, 17, 19, ... 23. Each number in the sequence is a consecutive prime number.

1, 1, 2, 3, 5, 8, 13, 21, 34, ... 55. Starting with 2, each number is the sum of the previous three.

1, 1, 2, 4, 7, 13, 24, ... 44. Starting with 4, every number is the sum of the previous three. I did these before I looked up the answers. This is the only one I missed.

3, 9, 27, 81, 243, 729, ... 2187. The numbers are in ascending powers of 3.

16807, 2401, 343, 49, ... 7. The numbers are in descending powers of 7.