3.1
Sequences
Numbers which are written in order, in a certain order, and increase equally with time are called *arithmetical sequences*. The next number in the order can be calculation by studying the earlier numbers pattern.
A simple arithmetical sequence can look like this:
1, 3,
5, 7, 9, ...
What number do you think comes after 9? If we look at the pattern for the sequence, it can help us to find the right continuation. The key to seeing the patter is that you examine how big a difference there is between the numbers.
1. Examine the difference between the first two numbers: 3 - 1 = 2
2. Examine the difference of the following two numbers: 5 - 3 = 2
3. Continue on a few numbers: 7 - 5 = 2 and 9 - 7 = 2
As you see, you add two to the last number. The sequence consists then of the odd number. Sequence: 1, 3, 5, 7, 9, …
Pattern: |
3 - 1 = 2 |
5 - 3 = 2 |
7 - 5 = 2 |
9 - 7 = 2 |
... |
**1,
3, 5, 7, 9, 11, 13**, **...**
We can take another example and do the same thing:
**1, 2, 4, 7, 11, ...**
We look at the patter for the sequence:
Pattern: |
2 - 1 = 1 |
4 - 2 = 2 |
7 - 4 = 3 |
11 - 7 = 4 |
... |
Here you look at the increase between the terms is not equally large the entire time. Then it is *not* an arithmetic sequence. However, it is a systematic increase and then we only call these *sequences*.
Now you know the difference between an arithmetic sequence and a sequence. |