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Sequences

Sequences. A list of numbers in a certain order. What is a sequence?. What is a term?. One of the numbers in the sequence. A sequence in which each term is found by ADDING the same number to the previous term. What is an arithmetic sequence?. 4, 8, 12 , 16, 20…………. +4. +4.

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Sequences

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  1. Sequences

  2. A list of numbers in a certain order. What is a sequence? What is a term? One of the numbers in the sequence.

  3. A sequence in which each term is found by ADDING the same number to the previous term. What is an arithmetic sequence? 4, 8, 12 , 16, 20………….. +4 +4 +4 +4

  4. The difference between each number, or what you add each time. What is the common difference? 4, 8, 12, 16, 20………….. 4 is the common difference How do you find it? The 2nd term minus the 1st term.

  5. Arithmetic Sequence Add the same number each time This is called the common difference examples 2, 4, 6, 8, … common difference is 2 50, 40, 30, 20… common difference is -10

  6. Arithmetic Sequences • 4, 7, 10, 13,… • Common difference: + 3 • 27, 24, 21, 18,… • Common difference: -3 • 5, 20, 35, 50,… • Common difference: + 15

  7. Arithmetic Sequences areLinear Patterns Line ar When you graph the pattern it makes a line It goes up or down gradually.

  8. A sequence in which each term can be found by MULTIPLYING the previous term by the same number. What is a geometric sequence? 3, 9, 27 , 81, 243………….. x3 x3 x3 x3

  9. The ratio between each number in the sequence, or what you multiply by each time. What is the common ratio? 2, 8, 32, 128, 512………….. 4 is the common ratio How do you find it? The 2nd term divided by the 1st term.

  10. Geometric Sequence Multiply by the same number each time This is called the common ratio examples 1, 4, 16, 64, … common ratio is x 4 400, 200, 100, 50, … common ratio is xor x o.5

  11. Geometric Sequence • 4, 8, 16, 32, 64, 128,… • Common ratio: x 2 • 2000, 1000, 500, 250, 125, 62.5,… • Common ratio: x ½ or x 0.5 • 6, 24, 96, 384, 1536, 6144,… • Common ratio: x 4

  12. Geometric Sequences areExponential Patterns ial Exponent When you graph the pattern it makes a steep curve It goes up or down fast!

  13. Make your own patterns Geometric Arithmetic • 1st term: 1, n + 2 • 1st term: 1000, n + (-50) • 1stterm: 12, n + 6 • 1st term: 81, n + (-9) • 1st term: 13, n + 5 • 1st term: 20, n + (-4) 1st term: 1, 2n 1st term: 1000, 0.5n 1st term: 3, 3n 1st term: 390,625, 0.2n 1st term: 1, 4n 1st term: 100, 1.5n

  14. Consecutive Terms: terms that are next to each other Variable Expression: can show the rule of a pattern Examples: 2, 4, 6, 8… n+2 8, 6, 4, 2… n + (-2) 2, 4, 8, 16… 2n16, 8, 4, 2… 0.5n

  15. Is this an arithmetic or geometric sequence? 10, 15, 20, 25, 30…… Arithmetic Sequence +5 5 is the common difference 1

  16. Is this an arithmetic or geometric sequence? 2, 12, 72, 432, 2,592…… Geometric Sequence x6 6 is the common ratio

  17. What is the next term in this sequence?5, 20, 80, 320 , _____ x4 x4 x4 x4 1,280

  18. What is the next term in this sequence?5, -1, -7 -13 , _____ -6 -6 -6 -6 -19

  19. What is the next term in this sequence?-3, 6, -12, 24 , _____ X-2 X-2 X-2 X-2 -48

  20. What is the next term in this sequence?-400,-380,-360,-340 , ____ +20 +20 +20 +20 -320

  21. What is the next term in this sequence?100, 75, 50 , 25____ -25 -25 -25 -25 0

  22. What is the next term in this sequence?12, -48, 192 , -768____ x-4 x-4 x-4 x-4 3,072

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