About this video
Two sequences are built from starting numbers and rules: Sequence x starts at 1 and adds 1 (1, 2, 3), and Sequence y starts at 5 and adds 5 (5, 10, 15). The terms are plotted as ordered pairs, and the video shows that each y term is 5 times the matching x term.
You'll be able to
- generate terms of a sequence from a starting number and a rule.
- make ordered pairs from two sequences and plot them.
- describe the relationship between corresponding terms of two sequences.
Key words
- sequence
- A list of numbers made by following a rule, like 'start at 1 and add 1'.
- rule
- The instruction that tells you how to get the next number, such as 'add 5'.
- ordered pair
- Two numbers written as (x, y) that show a point on a graph.
- term
- One number in a sequence, like the first, second or third term.
Transcript
Voiceover: You are given the following starting numbers and rules for two sequences of numbers. The first sequence, Sequence x, starting number should be one, and then the rule is add one. Sequence y, starting number should be five, and then the rule should be add five.
Fill in the table with the first three terms of x and y. Then plot the ordered pairs (x,y) on the graph below. So let's see, Sequence x. They say, the starting number, the starting number should be one. So the starting number is one, and then the rule, to get to the next number, you just add one.
So, one plus one is two. Two plus one is three. Fairly straight forward. Now, let's look at Sequence y. They're saying the starting number should be five. Starting number five, and then the rule is, to get the next term, we just add five. So, five plus five is ten, ten plus five is fifteen.
Now they want us to plot these things. Let's see, we plot them as ordered pairs, so we're going to have the point (1,5). When x is one, y is five. We see that there, x is one, y is five. When x is two, y is ten. When x is two, y is ten, and then when x is three, y is fifteen.
When x is three, y is fifteen, and wee see that. For every one we move to the right, for every one we increase in the horizontal direction, every one we increase in x, we increase five for y. We increase one for x, we increase five for y. So now we just have one last thing to answer.
The terms in Sequence y are blank, times the terms in Sequence x. So you immediately see, this term, five, is five times one. Ten is five times two. Fifteen is five times three, and it makes sense. You started five times higher, and here you added one each time, and we see that visually right over here, we add one each time, while here we add five times as much each time.
We add five each time. The terms in Sequence y are five times the terms in Sequence x. We got it right.
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