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Sequences and series

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  • 1. Examine the following lists below and group the lists into three: -2,-3,-4,-5,-6 2,7,8,11,19 3,6,9,12,15 1,3,9,27,81 0,1.1,4,5,7.7
  • 2. What is an arithmetic sequence?A sequence in whicheach term is found byADDING the samenumber to the previousterm.4, +4 8,+4 12 +4 16,+4 20………….. ,
  • 3. What is the common difference?The difference betweeneach number. Thisdetermines what is added toeach previous number toobtain the next number. 4, 8, 12, 16, 20………….. 4 is the common difference
  • 4. What is a geometric sequence?A sequence in whicheach term can be foundby multiplying theprevious term by thesame number.3,x3 9,x3 27x3 81, 243………….. , x3
  • 5. What is the common ratio?The number used to multiplyby each previous number toobtain the next number.2, 8, 32, 128, 512…………..4 is the common ratio
  • 6. Let’sPractice!
  • 7. Is this an arithmetic or geometric sequence? 10, 15, 20, 25, 30……Arithmetic Sequence +55 is the common difference
  • 8. Is this an arithmetic or geometric sequence?2, 12, 72, 432, 2,592……Geometric Sequence x6 6 is the common ratio
  • 9. What is the next term in this sequence? x4 x4 x4 x45, 20, 80, 320 , _____ 1,280
  • 10. What is the next term in this sequence? -6 -6 -6 -6 5, -1, -7 -13 , _____ -19
  • 11. What is the next term in this sequence? X-2 X-2 X-2 X-2 -3, 6, -12, 24 , _____ -48
  • 12. What is the next term in this sequence? +20 +20 +20 +20-400,-380,-360,-340 , ____ -320
  • 13. What is the next term in this sequence? -25 -25 -25 -25 100, 75, 50 , 25____ 0
  • 14. What is the next term in this sequence? x-4 x-4 x-4 x-412, -48, 192 , -768____ 3,072