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Hey there! Ready to become a pattern detective? Today, we will explore sequences and learn how numbers connect to each other.
A sequence is simply an ordered list of numbers. Each number in the list is called a term. To find the secret of a sequence, we analyze how one term changes to become the next.
Look at the sequence 2, 5, 8, 11. Each term is 3 more than the one before, so the common difference is 3. That lets us write an explicit rule for the nth term, a(n) = 2 + 3(n - 1), so we can jump straight to the 20th term without listing them all.
Not all sequences add the same value. Some patterns multiply, while others subtract. By analyzing the relationship between consecutive terms, you can predict any number that comes next!
Analyze the sequence 20, 17, 14, 11, ... to find the mathematical relationship and determine the next term.
- Compare the first term (20) and the second term (17). Notice that the numbers are decreasing.
- Calculate the difference between these terms: 20 minus 17 equals 3. This means we subtract 3.
- Check the next pair of terms to see if this relationship continues: 17 minus 14 equals 3.
- Confirm the rule by checking the next transition: 14 minus 11 equals 3. The rule is consistent.
- Apply the 'subtract 3' rule to the last known term (11) to find the next term: 11 minus 3 equals 8.
