HLRGAATPreISM_35799X_11_ch11

HLRGAATPreISM_35799X_11_ch11 - Chapter 11: Further Topics...

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Chapter 11: Further Topics in Algebra 11.1: Sequences and Ser ies 1. . The first five terms of the sequence are 2. . The first five terms of the sequence are 3. . The first five terms of the sequence are 4. . The first five terms of the sequence are 5. The first five terms of the sequence are 6. The first five terms of the sequence are 7. The first five terms of the sequence are 8. The first five terms of the sequence are 9. The first five terms of the sequence are 10. The first five terms of the sequence are 11. The terms of a sequence are numbered according to their position in the sequence; is the first term, is the second term, etc. So will be the n th term in the sequence for any positive integer value of n . 12. A sequence is a function which is defined on the positive integers. That is, the positive integers are the domain of the function and the terms of the sequence constitute the range of the function. 13. The sequence has 7 terms; it is finite. 14. The sequence has 30 terms; it is finite. 15. The sequence has 4 terms; it is finite. a n a 2 a 1 0, 3 5 , 4 5 , 15 17 , 12 13 . a 5 5 5 2 2 1 5 2 1 1 5 24 26 5 12 13 . a 4 5 4 2 2 1 4 2 1 1 5 15 17 ; a 3 5 3 2 2 1 3 2 1 1 5 8 10 5 4 5 ; a 2 5 2 2 2 1 2 2 1 1 5 3 5 ; a 1 5 1 2 2 1 1 2 1 1 5 0 2 5 2; 1, 7 6 , 1, 5 6 , 19 27 . a 5 5 4 1 5 2 2 1 5 2 1 2 5 19 27 . a 4 5 4 1 4 2 2 1 4 2 1 2 5 15 18 5 5 6 ; a 3 5 4 1 3 2 2 1 3 2 1 2 5 11 11 5 1; a 2 5 4 1 2 2 2 1 2 2 1 2 5 7 6 ; a 1 5 4 1 1 2 2 1 1 2 1 2 5 3 3 5 1; 2, ] 3, 4, ] 5, 6. a 5 5 1 ] 1 2 5 2 1 1 5 1 1 2 5 1 ] 1 2 4 1 6 2 5 6. a 4 5 1 ] 1 2 4 2 1 1 4 1 1 2 5 1 ] 1 2 3 1 5 2 5] 5; a 3 5 1 ] 1 2 3 2 1 1 3 1 1 2 5 1 ] 1 2 2 1 4 2 5 4; a 2 5 1 ] 1 2 2 2 1 1 2 1 1 2 5 1 ] 1 2 1 1 3 2 3; a 1 5 1 ] 1 2 1 2 1 1 1 1 1 2 5 1 ] 1 2 0 1 2 2 5 2; ] 2, 4, ] 6, 8, ] 10. a 5 5 1 ] 1 2 5 31 2 21 5 24 10. a 4 5 1 ] 1 2 4 2 4 5 8; a 3 5 1 ] 1 2 3 2 3 6; a 1 5 1 ] 1 2 2 2 2 5 4; a 1 5 1 ] 1 2 1 2 1 2; ] 2, 8, ] 24, 64, ] 160. a 5 5 1 ] 2 2 5 1 5 2 160. a 4 5 1 ] 2 2 4 1 4 2 5 64; a 3 5 1 ] 2 2 3 1 3 2 24; a 2 5 1 ] 2 2 2 1 2 2 5 8; a 1 5 1 ] 2 2 1 1 1 2 2; 0, 1 9 , 2 27 , 1 27 , 4 243 . a 5 5 a 1 3 b 5 1 5 2 1 2 5 a 1 243 b 1 4 2 5 4 243 . a 4 5 a 1 3 b 4 1 4 2 1 2 5 a 1 81 b 1 3 2 5 1 27 ; a 1 5 a 1 3 b 3 1 3 2 1 2 5 a 1 27 b 1 2 2 5 2 27 ; a 2 5 a 1 3 b 2 1 2 2 1 2 5 a 1 9 b 1 1 2 5 1 9 ; a 1 5 a 1 3 b 1 1 1 2 1 2 5 a 1 3 b 1 0 2 5 0; ] 3, ] 9, ] 27, ] 81, ] 243. a 5 3 5 243 a 4 3 4 81; a 3 3 3 27; a 2 3 2 9; a 1 3 1 3; 1, 2, 4, 8, 16. a 5 5 2 5 2 1 5 2 4 5 16 a 4 5 2 4 2 1 5 2 3 5 8; a 3 5 2 3 2 1 5 2 2 5 4; a 2 5 2 2 2 1 5 2 1 5 2; a 1 5 2 1 2 1 5 2 0 5 1; 3, 9, 15, 21, 27. a 5 5 6 1 5 2 2 3 5 27 a 4 5 6 1 4 2 2 3 5 21; a 3 5 6 1 3 2 2 3 5 15; a 2 5 6 1 2 2 2 3 5 9; a 1 5 6 1 1 2 2 3 5 3; 14, 18, 22, 26, 30. a 5 5 4 1 5 2 1 10 5 30 a 4 5 4 1 4 2 1 10 5 26; a 3 5 4 1 3 2 1 10 5 22; a 2 5 4 1 2 2 1 10 5 18; a 1 5 4 1 1 2 1 10 5 14;
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16. The sequence has 4 terms; it is finite. 17. The sequence has no last term; it is infinite. 18. The sequence has no last term; it is infinite. 19. The sequence is defined for integer values of n from 1 through 10; it is finite.
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HLRGAATPreISM_35799X_11_ch11 - Chapter 11: Further Topics...

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