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Describe the pattern. Find the next three numbers.

7. 0.7, 2.1, 6.3, 18.9,...
8. 0.13, 0.65, 3.25, 16.25,...
9. 2, 0.04, 0.0008, 0.000016, ...
10. 6, 1.8, 0.54, 0.162, ...

1 Answer

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Answer:

7. a[n] = 3·a[n-1]; 56.7, 170.1, 510.3

8. a[n] = 5·a[n-1]; 81.25, 406.25, 2031.25

9. a[n] = 0.02·a[n-1]; 0.00000032, 0.0000000064, 0.000000000128

10. a[n] = 0.3·a[n-1]; 0.0486, 0.01458, 0.004374

Explanation:

These sequences are all geometric sequences, so terms have a common ratio. That ratio can be found by dividing the second term by the first. The next term is found by multiplying the last term by the common ratio.

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7. ratio is 2.1/0.7 = 3. Each term is 3 times the last. The next three terms are ...

18.9×3 = 56.7, then 170.1 and 510.3

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8. ratio is .65/.13 = 5. Each term is 5 times the last. The next three terms are ...

16.25×5 = 81.25, then 406.25 and 2031.25

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9. ratio is .04/2 = .02. Each term is 0.02 times the last. The next three are ...

0.000016×0.02 = 0.00000032 = 3.2×10^-7, then 6.4×10^-9 and 1.28×10^-10

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10. ratio is 1.8/6 = 0.3. Each term is 0.3 times the last. The next three are ...

0.162×0.3 = 0.0486, then 0.01458 and 0.004374

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