Add-the-Previous-Two Patterns (Grades 5–6)
Some sequences build each term by adding the two before it — the famous Fibonacci pattern: 1, 1, 2, 3, 5, 8, 13. There's no single common difference or ratio; instead, the rule looks back two steps. To extend it, add the last two terms.
Understanding add-the-previous-two patterns
Some sequences build each term by adding the two before it — the famous Fibonacci pattern: 1, 1, 2, 3, 5, 8, 13. There's no single common difference or ratio; instead, the rule looks back two steps. To extend it, add the last two terms.
Key Idea
Some sequences build each term by adding the two before it — the famous Fibonacci pattern: 1, 1, 2, 3, 5, 8, 13. There's no single common difference or ratio; instead, the rule looks back two steps. To extend it, add the last two terms.
Seeing it in action
Worked example
Continue: 1, 1, 2, 3, 5, __.
Add the last two: 3 + 5 = 8.
Each new term uses the two before it.
Try a few
2, 3, 5, 8, __
8 + 5.
1, 4, 5, 9, __
9 + 5.
0, 1, 1, 2, 3, __
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Put the reasoning on paper.
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