To determine which sequence can be approximated by the expression \(4n^3\), first, we need to understand how to analyze each given sequence.
The expression \(4n^3\) grows very rapidly as \(n\) increases, so we should look for sequences whose values increase at a cubic rate.
Let's evaluate each provided sequence one at a time and compare it with \(4n^3\).
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Sequence: 10, 31, 78, 168
- n=1: \(4(1^3) = 4\)
- n=2: \(4(2^3) = 32\)
- n=3: \(4(3^3) = 108\)
- n=4: \(4(4^3) = 256\)
The first value \(10\) is close to \(4\), the second value \(31\) is close to \(32\), but the subsequent values deviate significantly from \(4n^3\).
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Sequence: 21, 47, 85
- Similar calculation shows values deviating from \(4n^3\).
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Sequence: 26, 38, 12
- The values deviate as n increases.
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Sequence: 10, 38, 106
- Again, doesn't fit \(4n^3\) as examined with cubic growth.
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Sequence: 10, 49, 142, ...
- Reviewing shows exponential deviation.
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Sequence: 10, 32, 74, 142
- Similar growth deviation is observed.
Through all sequences provided, it typically appears that none align closely with the \(4n^3\) growth pattern without significant deviation.
You might wish to try plotting your sequences and \(4n^3\) to visualize for exponential mismatch in growth. That said, given here they appear dramatically outpaced by cubic growth.
If you have additional context about specific sequences or patterns you're interested in, please share that and we can analyze further.
1 answer