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Homework Questions

Homework Questions. Number Patterns. Find the next two terms, state a rule to describe the pattern. 1, 3, 5, 7, 9… 16, 32, 64… 50, 45, 40, 35… -3, -7, -11, -15…. Sequence Notation. A sequence is an ordered list of numbers – each number is a term . State the first 5 terms: a n = n

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Homework Questions

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  1. Homework Questions

  2. Number Patterns • Find the next two terms, state a rule to describe the pattern. • 1, 3, 5, 7, 9… • 16, 32, 64… • 50, 45, 40, 35… • -3, -7, -11, -15…

  3. Sequence Notation • A sequence is an ordered list of numbers – each number is a term. • State the first 5 terms: • an = n • (plug in 1, 2, 3, 4, 5) • 1, 2, 3, 4, 5

  4. an = 4n an = 2n-3 an = |1-n2| an = an = More Examples

  5. Recursive v. Explicit

  6. Definition • Recursive Formula – a sequence is recursively defined if the first term is given and there is a method of determining the nth tem by using the terms that precede it. • English– if you can use the term before it to figure out what comes next • Ex: {-7, -4, -1, 2, 5, …}

  7. Examples of Recursive • {-9, -4, -2, 0, 2, …} • {-4, -8, -16, -32, -64, …} • {6, 11, 16, 21, 26, …} • {8, 4, 2, 1, …}

  8. Definition • Explicit Formula – a formula that allows direct computation for any term for a sequence • English – you don’t need to term prior in order to figure out what the nth term is going to be. • Ex: {8, 9, 10, 11, 12, …} • an= n + 7

  9. Examples of Explicit • {-3, 1, 5, 9, …} • {1, 4, 9, 16, …} • {7, 9, 11, 13, …} • {24, 20, 16, 12, …}

  10. Arithmetic Sequences

  11. Arithmetic Sequences • In an arithmetic sequence, the difference between consecutive terms is constant. • The difference is called the common difference. • To find d: 2nd term – 1st term

  12. Arithmetic? • 2, 4, 8, 16 • 6, 12, 18 • 48, 45, 42 • 2, 5, 7, 12

  13. Recursive Formula an = an-1 + d use if you know prior terms Explicit Formula an = a1 + (n-1)d an = nth term a1 = 1st term n = number of terms d = common difference Arithmetic Sequence Formulas

  14. Examples • Find the 20th term of each sequence • 213, 201, 189, 177… • .0023, .0025, .0027…

  15. More examples • Find the 17th term of the sequence: • a16 = 18, d = 5

  16. Find the missing term • Use arithmetic mean = average! • 84, _______, 110 • 24, _______, 57

  17. Geometric Sequences

  18. Geometric Sequences • In a geometric sequence, the ratio between consecutive terms is constant. • This ratio is called the common ratio. • To find r:

  19. Geometric, Arithmetic, Neither?(find the next 2 terms if so) • 5, 15, 45, 135… • 15, 30, 45, 60… • 6, -24, 96, -384… • 8, 20, 32, 44…

  20. Geometric Sequences Formulas • Recursive Formula • an = an-1 r • Explicit Formula • an = a1 rn-1

  21. Find the 19th term… • 11, 33, 99, 297… • 20, 17, 14, 11, 8…

  22. FYI - Graphs • Arithmetic Graphs are linear • Geometric Graphs are exponential

  23. Geometric Mean • Geometric Mean = • 20, _____, 80 • 3, ____, 18, 75 • 28, ____, 5103

  24. Homework • WORKSHEET! • We need to talk about numbers 16-20 though, so wait on me!

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