My son and I played a game tonight. Each of us took turns giving patterns of numbers to the other who was to guess what the next number in the pattern was. Here are some of our number patterns we challenged each other with:
1, 2, 4, 8, …
1, 3, 5, …
2, 10, 18, …
1, 3, 9, …
150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900, 950, 1000, 1500, ….
3, 5, 4, 4, 4, 4, … (this one is sneaky, so I’ll give away the answer. One has three letters, three has five letters, five has four letters, four has four letters, and so on. My son came up with this one. An aside: does this sequence always end up with a repeating four, no matter which number you begin with?)
I finally stumped my son with the following:
1, 1, 2, 3, 5, 8, 13, …
Math Thinking 
Is the 5th one wrong – should the last number be 1050 – or is the pattern more subtle than the pattern I see?
I told my son the next one in his pattern was 2000, and he groaned… but didn’t say i was wrong. š