The given sequence is $14, 10, 28, 17, 49,$. Let's analyze the pattern step by step to find the next term.

1. From 14 to 10: Subtract 4. $14 - 4 = 10$

2. From 10 to 28: Add 18. $10 + 18 = 28$

3. From 28 to 17: Subtract 11. $28 - 11 = 17$

4. From 17 to 49: Add 32. $17 + 32 = 49$

Looking at this pattern:

• The subtraction step seems to decrease by 7 each time (-4, -11).
• The addition step seems to increase by 14 each time (+18, +32).

If the pattern continues, the next step should involve subtracting 7 more than the previous subtraction, and then adding 14 more than the previous addition.

So:

1. The next subtraction should be $11 + 7 = 18$.
2. Subtracting 18 from 49: $49 - 18 = 31$

Therefore, the next term in the sequence is 31.

Would you like more details, or do you have any other questions?

Here are 5 related questions:

1. Can you identify the general rule or formula for this sequence?
2. How would the sequence continue after 31?
3. What happens if the pattern of addition and subtraction changes in the sequence?
4. How does this sequence compare to an arithmetic sequence?
5. What would happen if we introduced multiplication or division into this sequence?

Tip: When analyzing sequences, alternating patterns (e.g., addition/subtraction or multiplication/division) often reveal more complex structures.