Number sequences

​[chuckles] That's a good one. Okay, here's another one: name the next number in the series. ​ ​Two, four, six... Eight. Correct, it's a grasshopper on a chessboard only jumping on the black squares. ​ ​Okay, I've got one. One, zero, two, one, three, two.  ​ ​Decrease by one, increase by two, minus one plus two.

Every other time we deduct one then add two and so on, the next number is four. ​ ​Right. It's an ant climbing up a slippery leg of a chair. For every two centimeters it climbs up, it slips down one centimeter. ​ ​Good, my turn. One, four, nine, sixteen. ​ ​Uh, it's plus three, plus five, plus seven. The difference increases by two every time, so the next one is plus nine, 25. ​ ​Twenty-five is right, but I thought like this: it's the term number squared. ​ ​Term number? ​ ​Yes, the first integer is number one.

The second integer is number two. The third is number three, and so on. Then take that term number squared, or times itself. This is my number series. ​ It's a row of squares where the length of the square side ​That's right. increases by one between each square in the series and to the next square.

I've got a new one. Zero, one, one, two, three, five. ​ ​The numbers increase, but not by the same amount for each step. No, I cannot guess. ​ ​Every number is the sum of the two preceding numbers. Zero plus one is one, one plus two is three, two plus three is five. Okay, eight.

The next number is eight, but what does it represent? ​ ​A snail shell. The radius of the shell increases by the corresponding value for every quarter of a turn. But I cheated a bit because I didn't make this sequence up myself. It is called the Fibonacci Sequence. It's 800 years old.

Okay, so this is how you do it using the number terms. The term number N, is the sum of the terms that places N minus one and N minus two. That's right and here's another one: one, two, three, four, five. ​ ​That's too easy. Six, seven, eight, nine, ten, eleven, twelve, thirteen.