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, ...

9514 1404 393

  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

Step-by-step 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