\(1,~2,~3,~5,~8,~13,~21,~34,\ldots\)

• These numbers are increasing.
• The gaps between the numbers are getting larger.
• These numbers are not random.

Solution

We generate numbers in this list by adding the two previous numbers.

\(1,~2,\class{timed add4-cover remove5-cover}{\class{hl2}{\xrightarrow{1+2=3}}}3,\class{timed add4-cover remove6-cover}{\class{hl2}{\xrightarrow{2+3=5}}}5,\class{timed add4-cover remove7-cover}{\class{hl2}{\xrightarrow{3+5=8}}} 8,\ldots\)

These numbers occur often in nature! 

\(1,~2,~3,~5,~8,~13,~21,~34,\ldots\)

Pinecones

Broccoli

Daisies

These are called the Fibonacci numbers.

• Given a sequence, describe a pattern rule.
• Identify the position of an item in a sequence.
• Represent information about patterns in a table.