What should come in place of the question mark (?) in the given series? 74, 83, 101, 128, ?, 209
164
To solve the sequence 74, 83, 101, 128, ?, 209, we need to find the pattern or rule that applies to this series and determine the missing number.
Let's examine the difference between successive terms:
- Difference between the first and second term: \(83 - 74 = 9\)
- Difference between the second and third term: \(101 - 83 = 18\)
- Difference between the third and fourth term: \(128 - 101 = 27\)
We observe that the differences themselves form a pattern: 9, 18, 27.
These differences are multiples of 9: \(9 \times 1, 9 \times 2, 9 \times 3\).
Following this pattern, the next difference should be \(9 \times 4 = 36\).
Add this difference to the last known term of the series:
\(128 + 36 = 164\)
Therefore, the missing number in the series is 164.
Thus, the sequence becomes: 74, 83, 101, 128, 164, 209.
All options are considered, and only 164 fits the identified pattern. Therefore, the correct answer is 164.
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