Math Problem Statement

2,3,8,31,?

Solution

To solve the sequence 2,3,8,31,?2, 3, 8, 31, ?, let's look for a pattern.

One possible approach is to check the difference between consecutive terms:

32=13 - 2 = 1 83=58 - 3 = 5 318=2331 - 8 = 23

Now, let's look at the differences between these differences:

51=45 - 1 = 4 235=1823 - 5 = 18

Notice that the differences between the differences seem to be increasing as well. This suggests a possible quadratic pattern.

The next difference could follow the same pattern of increasing by an additional factor. If the second difference increased by 1414 (from 4 to 18), adding the next expected increase (of 3232):

23+32=5523 + 32 = 55

Adding this to the last term:

31+55=8631 + 55 = 86

So, the next term in the sequence should be 86.

Would you like further details, or have any questions? Here are some questions for you:

  1. Would you like to explore another sequence?
  2. Can I help you find a formula for this sequence?
  3. Do you want to analyze the pattern using a different method?
  4. Would you like to see the entire process in a step-by-step manner?
  5. Do you want to explore more complex sequences?

Tip: When dealing with sequences, always look for patterns in differences or ratios between terms!

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Math Problem Analysis

Mathematical Concepts

Sequences and Series
Pattern Recognition

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12