Lesson 7 — Activity 3: Creating Formulas for Simple Patterns


Getting Ready


So far in this lesson, you have looked at finding out what kind of pattern you have and figuring out what you have to do to each number to get the next number in the pattern.

Here's an example of the patterns you have been working on.
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In this activity, you are going to take that a step further and create formulas for patterns.

Let's say you have the pattern 2, 4, 6, 8. What can you tell by looking at the numbers?
  • First off, you are adding 2 to each number to get the next number.
  • Second, because you are adding, you know that you have an arithmetic sequence.
It would not be hard to figure out what the next term (next number) in the sequence is, or for that matter, what the next three numbers are.

However, it gets a bit harder if you are asked for the hundredth term in the sequence. This is where a formula can be very helpful.
Each number in a sequence is given a term number.
In the pattern we've just looked at, 2 is term one (t1), 4 is term two (t2), 6 is term three (t3), and 8 is term four (t4). Any unknown term is written as tn.
If you wish, you could write it like this:

2,    4,    6,   8
t1,  t2,   t3,  t4

 
If you wanted to make a formula to find the hundredth term in the pattern, you could do it like this:

t100 = 2n


t100 = 100 x 2


t100 = 200

Notice that the n in the formula is replaced by the term number. The hundredth term in the pattern is 200.