The given sequence is: 20, 40, 42, 82, 83, 166, ...

Let's analyze the pattern by looking at the differences between consecutive terms:

• 40 - 20 = 20
• 42 - 40 = 2
• 82 - 42 = 40
• 83 - 82 = 1
• 166 - 83 = 83

We notice that the differences alternate between large values and small values:

• Large differences: 20, 40, 83
• Small differences: 2, 1

It seems the large differences are growing roughly in a certain pattern, and the small differences alternate between 2 and 1.

Let's hypothesize that the next step follows this alternating pattern. We could expect another small difference of 2, and the large difference may continue increasing.

So, the next term could be:

• 166 + 2 = 168 (if the small difference of 2 continues)

Next, we might expect the next large difference to increase by a similar pattern.

Would you like further details or a deeper explanation? Feel free to ask!

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Here are 5 related questions to explore further:

1. What other patterns can be identified in sequences with alternating differences?
2. How do you recognize arithmetic and geometric progressions?
3. How do you predict the next terms in a sequence with multiple patterns?
4. What role do odd and even positions in a sequence play in forming patterns?
5. How can recurrence relations be used to model sequences?

Tip: Always start by analyzing the differences between consecutive terms when identifying a pattern.