SOLUTION: What is the Multiplication Sequence for 405,__, ___, ___, 5? Thanks so much

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Question 644468: What is the Multiplication Sequence for 405,__, ___, ___, 5? Thanks so much
Answer by MathTherapy(10557) About Me  (Show Source):
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What is the Multiplication Sequence for 405,__, ___, ___, 5? Thanks so much

As this is a geometric sequence, we use the formula: a%5Bn%5D+=+a%5B1%5Dr%5E%28n-1%29

To determine r, or ratio in the sequence, we have: a%5Bn%5D+=+a%5B1%5Dr%5E%28n+-+1%29, with n = 5; a%5Bn%5D+=+5; a%5B1%5D+=+405

5+=+405r%5E%285+-+1%29

5+=+405r%5E4

5%2F405+=+r%5E4

1%2F81+=+r%5E4

root%284%2C+1%2F81%29+=+r

1%2F3+=+r
The ratio or r of this sequence = highlight_green%281%2F3%29

You can use the ratio to determine terms 2 through 5. As term 5 was given, when the ratio is applied, term 5 should equal 5.

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