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

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

\[
3 - 2 = 1
\]
\[
8 - 3 = 5
\]
\[
31 - 8 = 23
\]

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

\[
5 - 1 = 4
\]
\[
23 - 5 = 18
\]

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 \(14\) (from 4 to 18), adding the next expected increase (of \(32\)):

\[
23 + 32 = 55
\]

Adding this to the last term:

\[
31 + 55 = 86
\]

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!

Explore the sequence 2, 3, 8, 31 and learn how to predict the next term using pattern recognition and mathematical analysis. This problem involves identifying differences between terms and predicting the next term in the sequence. Suitable for Grades 9-12.

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