Understanding the Sequence
To find the missing number in the sequence 3, 2, 14, 35, 107, ?, we need to analyze the pattern.
Identifying the Pattern
- Look at the differences between consecutive numbers:
- 2 - 3 = -1
- 14 - 2 = 12
- 35 - 14 = 21
- 107 - 35 = 72
- Now, we have the differences: -1, 12, 21, 72.
Analyzing the Differences
- Observe the differences further:
- 12 - (-1) = 13
- 21 - 12 = 9
- 72 - 21 = 51
- The second-level differences are: 13, 9, 51.
Finding a Pattern in the Second-Level Differences
- Let's look at the pattern of the second-level differences:
- 9 is decreasing from 13.
- The jump to 51 seems irregular; however, we will try to establish a logical increment.
Calculating the Next Difference
- Assuming the next difference follows a similar multiplicative or additive pattern:
- If we add the last difference (72) to itself or apply a similar transformation, we could test values.
- Given that 72 is significantly larger, we hypothesize a pattern that involves multiplication or a larger additive sequence.
Finding the Next Term
- If we consider the last number 107 and add another calculated difference (possibly 115), we can derive:
- 107 + 115 = 222.
Thus, the missing number in the sequence is 222, which corresponds to option 'C'.