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a.
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b.
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c.
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d.
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e.
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f.
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g.
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1.
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r = 2
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r = 0.5
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Not geometric
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r = 0.8
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r = w
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r = √3
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r = -3
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2.
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160, 320
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1.25, 0.625
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Not geometric
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40.96, 32.768
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w5, w6 |
9, 9√3
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243, -729
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3.
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1024
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0.5625
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8192
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47.59 (4s.f.)
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0.00390625
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1397.5
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1048576z21
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4.
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2n
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3n
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 |
q x 3n − 1
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 |
 |
6 x (-1)n-1
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5. r = 2, a = 0.5 and the sequence is 0.5, 1, 2 ,4, ... 0r r = -2, a = -0.5 and sequence is -0.5, 1, -2, 4,...
6.r = 1/3, a = 27 and the sequence is 27, 9, 3, 1, ...
7. 768 is the 8th term.
8. 4096 is the 7th term.
9. He would be doing 32, 768 press-ups and probably be very fit... or dead!
10. 4092
11. 6560
12. 27.95
13. 
14. 23.52
15. -682
16. 0
17. 739.93
18. 60
19. 10.67 ( to 4 sig. fig.)
20. 32
21. First term is 8
22. Common ratio is 2, first term is 2 and the sum of the 10th terms is 2046.
23. $10, 737, 418, 230
24. In six years time he will be 181 cm tall and his average height over the six years was 161 cm. (to 3 s.f.)
25. a. The differences between data values are not constant, but show a definite decrease with time:
b. The ratios between consecutive years are consistent with a constant ratio of 0.98, therefore it is a gemetric sequence.
c. L = 0.8(0.98)n-1
d. Total height = 18.68 m
e. Expected maximum = 40.5 metres
