How to Use Algebra to Describe Number Sequences

Hi, I'm Rebecca. And in this film, we're going to look at using algebra to describe sequences. So let's have a look at one in this sequence. Here we have a series of dots that make up rectangles. And we have been asked the question, what would you like the fifth rectangle to look like? And can you write a rule using algebra? So at this point, you want to encourage your pupils to have a look at the pattern. Can they see a pattern between the number of dots increasing each time, or is there a link between the number in the sequence and the number of dots? Now, if we look at this one, you can see that the sequence increases by two dots each time. And the link between the number in the sequence is that if you multiply that by two, it tells you the number of dots. So for the fifth one in our sequence, we know that we need to multiply five by two. So we need 10 dots. So we've got 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. And then that gives us our fifth sequence. Now, to write this as a rule, using algebra, we can use N to represent any number. So here we multiplied five by two. So we can write this as a rule, saying two times N. For more complicated patterns and sequences, we want to encourage children to think about what increases each time and what remains constant in this sequence. Here we have the formula three times n plus one. And the N represents any number. Now, the thing that increases each time is the orange dots, and that's the three times N. The plus one is the red dot that remains constant. So here, if we were trying to find the 100th pattern in the sequence, we can use our formula to work it out. 3 times n with n being 100 would be 300. And then we need to add on our one red dot that is the constant. So we can use this formula to work out that our hundredth pattern in the sequence would have 301 dots. So there you go. That's how to use algebra to describe sequences.