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The World is Full of Patterns

The World is Full of Patterns. By examining a wide range of patterns, we notice regularity, variety, and the ways things interconnect. We also see that certain patterns occur again and again. Can you name some patterns that occur naturally?. The World is Full of Patterns. Patterns and Sequences.

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The World is Full of Patterns

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  1. The World is Full of Patterns By examining a wide range of patterns, we notice regularity, variety, and the ways things interconnect. We also see that certain patterns occur again and again. Can you name some patterns that occur naturally?

  2. The World is Full of Patterns

  3. Patterns and Sequences A Sequence is an ordered list of numbers or objects. Each number or object in a sequence is called a term.

  4. Complete the Sequences 7, 11, 15, 19, 23, _____, _____, _____ 27 31 35 -12, -4, 4, 12, _____, _____, _____ 20 28 36

  5. An Arithmetic Sequence is a pattern formed by adding the same number to each previous term to find the next term. This number is called the Common Difference. The common difference must always the same.

  6. Determine if each sequence Arithmetic. 16, 14, 13, 11, 10, ….. NO 2, 3, 5, 8, 12, 17, ….. NO YES! 1.5, 3, 4.5, 6, 7.5, ……

  7. Find the 100th term to this sequence: 5, 9, 13, 17, …….

  8. Formula for finding the nth term of an Arithmetic Sequence. an = a1+ (n – 1) d Common difference The 1st term The nth term

  9. Find the 25th term. 8, 10, 12, 14, 16, ….. 56 Find the 50thterm. 2, 9, 16, 23, 20, .... 345

  10. Complete these Sequences: 1, 2, 4, 8, 16, _____, _____, _____ 32 64 128 2, 6, 18, 54, _____, _____, _____ 162 486 1458 Now, find the 100th term to these sequences.

  11. A Geometric Sequence is a pattern formed by multiplying the same number to each previous term to find the next term. This number is called the Common Ratio. The common ratio must always the same.

  12. Formula for finding the nth term of an Geometric Sequence. an = a1rn-1 Common ratio The 1st term The nth term

  13. Find the 12th term. 3, 6, 12, 24, 48, ….. 6144 Find the 91stterm. 1/5, -1/5, 1/5, -1/5 .... 1/5

  14. Compare Arithmetic Sequences and Geometric Sequences. Compare Arithmetic Sequences and Linear Functions. Compare Geometric Sequences and Exponential Functions.

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