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# Sequences and series

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### Sequences and series

1. 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. 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. 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. 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. 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. 6. Let’sPractice!
7. 7. Is this an arithmetic or geometric sequence? 10, 15, 20, 25, 30……Arithmetic Sequence +55 is the common difference
8. 8. Is this an arithmetic or geometric sequence?2, 12, 72, 432, 2,592……Geometric Sequence x6 6 is the common ratio
9. 9. What is the next term in this sequence? x4 x4 x4 x45, 20, 80, 320 , _____ 1,280
10. 10. What is the next term in this sequence? -6 -6 -6 -6 5, -1, -7 -13 , _____ -19
11. 11. What is the next term in this sequence? X-2 X-2 X-2 X-2 -3, 6, -12, 24 , _____ -48
12. 12. What is the next term in this sequence? +20 +20 +20 +20-400,-380,-360,-340 , ____ -320
13. 13. What is the next term in this sequence? -25 -25 -25 -25 100, 75, 50 , 25____ 0
14. 14. What is the next term in this sequence? x-4 x-4 x-4 x-412, -48, 192 , -768____ 3,072