Sequences and series
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The document contains information about arithmetic and geometric sequences. It defines an arithmetic sequence as one where each term is found by adding the same number to the previous term, called the common difference. A geometric sequence is one where each term is found by multiplying the previous term by the same number, called the common ratio. Examples are worked through and questions are asked about finding the next term in various sequences.
Sequences and series
- 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 which each term is found by ADDING the same number to the previous term. 4, +4 8,+4 12 +4 16,+4 20………….. ,
- 3. What is the common difference? The difference between each number. This determines what is added to each previous number to obtain the next number. 4, 8, 12, 16, 20………….. 4 is the common difference
- 4. What is a geometric sequence? A sequence in which each term can be found by multiplying the previous term by the same number. 3,x3 9,x3 27x3 81, 243………….. , x3
- 5. What is the common ratio? The number used to multiply by each previous number to obtain the next number. 2, 8, 32, 128, 512………….. 4 is the common ratio
- 7. Is this an arithmetic or geometric sequence? 10, 15, 20, 25, 30…… Arithmetic Sequence +5 5 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 x4 5, 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-4 12, -48, 192 , -768____ 3,072