Answered

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Identify a pattern in each list of numbers. Then use this pattern to find the next number. 5, 12, 33, 96, 285, ___

Sagot :

sqdancefan

Answer:

  852

Step-by-step explanation:

You want the next number in the pattern that starts with 5, 12, 33, 96, 285.

Pattern

When looking for patterns in sequences, it is often useful to consider first differences and the relations between them.

  12 -5 = 7

  33 -12 = 21

  96 -33 = 63

  285 -96 = 189

We notice that these differences have a common ratio of 3. This suggests the next difference will be 189×3 = 567.

The next number in sequence is 285 +567 = 852.

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Additional comment

When differences have a common ratio, an exponential sequence is indicated. These differences have a ratio of 3, but are not powers of 3, so the exponential term needs additional components to completely describe the sequence. We expect there are horizontal and vertical offsets involved.

Exponential regression gives the explicit formula as ...

  y = (3 +7·3^(x-1))/2

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