What makes a sequence, more than a bunch of numbers is the order, the numbers feature. I think of it as a cloak room, of a bowling clubs, cool feature play theater nightclub. There is a ticket with a number for each item. While, the analogy breaks down as the items are all different, then two people could have the same coat or back. The point is, the items in a sequence are labeled, and so there is an order. In a different day, we have a different sequence of things. When we deal with sequences of numbers, we care about the variation of numbers as the labels, ticket numbers increase. So, a sequence is an ordered list of numbers. Here are some examples of sequences, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday ending there. One minus one, one minus one, one minus one, one minus one and so on. Three, three, three, three, three and carry on like that. One, 11, 111, 1111 and so on. Or five, four, three, two, one, zero ending there. As a computer scientist, one of the basic uses of sequences, will be tapping into their patterns in order to be able to use them computationally. As I mentioned in the introduction, there are many other applications. But for this video, let's be pattern hunters. So, take a moment to go through the sequences presented, make some notes on the patterns found, and your own way of describing each of these sequences in words. Let's gather our thoughts on this. The first is the sequence of week days starting on Monday. Note that it is a finite sequence. It only has seven terms. The second sequence is infinite. As implied by the dot-dot-dot which says continuing in the same pattern. So, the pattern is alternating, alternating between one and negative one. Or you could say, beginning in one, subtract two, then add two and so on. Another way of saying it would be you start in one, and you alternate between, subtracting two and adding two. There is more than one way of describing it. The third sequence is a constant sequence of threes, and is also infinite. The fourth could be described as begin with one, then write another one next to it and carry on like this. Or we could say instead, on each position, write that many ones. So, one, one in the first position, two ones in the second position, three ones in the third position and so on. Or you may be thinking of place value. Add up consecutive powers of ten. So, starting one and add 10 for the next term, then a 100 and so on. Or you could even be thinking of binary. Anyway, I'll let you think of how to express this pattern. The fifth is a finite sequence, a countdown from five or starting five, and subtract one to get next term, stop at zero. For the sixth, it is an infinite sequence. There is a pattern of multiplying by three each time. So we could say, starting from three, obtain the next term by multiplying the previous term by three. Another way could be consecutive powers of three. Let's have another look at sequences. I want you to write down the patterns you find, so that you can describe them to another person. Here are the sequences. We're going to discuss them after the pause. Now, the first, is a sequence of consecutive square numbers starting from the square of one. The second, is a sequence of consecutive cube numbers, starting from the cube of one. The third, is a sequence of fractions of ratios of consecutive numbers. The first term is one over two, the second term, is the second number over the third, so two over three and so on. So, the nth term is n divided by n plus one. We start needing formal mathematical language, to define these sequences precisely. Now, the fourth, is zero point as many nines as the order of the term. Does that sound complicated? The fifth could be the sequence of prime numbers. There is no formula for this. The sixth sequence seems to be a power of two, and the number that comes next. Then the next power of two, and the number one over it and so on. You probably with me. We need a better way of formalizing these patterns. Join me in the next video after the quiz.