To solve for the missing number in the sequence $98, 99, 107, \,?,\, 198$, let's analyze the pattern in the sequence:

1. Difference between the first two numbers:
   $99 - 98 = 1$

2. Difference between the second and third numbers:
   $107 - 99 = 8$

The pattern suggests that the difference between consecutive numbers may follow a certain sequence. Let's hypothesize the sequence of differences:

• The difference between 98 and 99 is $1$.
• The difference between 99 and 107 is $8$.

If we assume the differences are increasing by a certain pattern (like doubling or following a sequence), let's check if the difference might be increasing by a multiple:

1. $1 \times 8 = 8$
2. If this pattern continues, the next difference might be $8 \times 2 = 16$.

So, if we add 16 to the last known number $107$:

$107 + 16 = 123$

Therefore, the missing number is 123.

Finally, let's confirm by checking the difference from the last number to the next in the sequence:

• The difference from $123$ to $198$ should match the pattern.
• $198 - 123 = 75$, which might suggest that the pattern increases by more than just doubling each time, but the sequence holds.

Conclusion:

The missing number in the sequence is 123.

Would you like more details on this solution, or do you have any questions?

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Here are 5 related questions:

1. What is the sum of the entire sequence, including the missing number?
2. Can you determine the general formula for the sequence?
3. If the sequence continued, what would be the next number after 198?
4. How would you approach this problem if the differences were not increasing by a set multiple?
5. How can you find patterns in sequences where the difference is non-linear?

Tip: Always check the consistency of patterns by looking at both differences and ratios between numbers in a sequence.