A sequence of numbers is presented below, in which one value does not follow the correct mathematical pattern.
Identify the incorrect term from the given sequence.
128, 144, 127, 146, 123, 152, 121
Correct Answer :
128
Solution :
The correct answer is 128 — it is the incorrect term in the given sequence.
The sequence given is:
128, 144, 127, 146, 123, 152, 121
Step 1: Calculate the differences between consecutive terms.
144 - 128 = 16
127 - 144 = -17
146 - 127 = +19
123 - 146 = -23
152 - 123 = +29
121 - 152 = -31
So the differences are: +16, -17, +19, -23, +29, -31
Step 2: Analyze the absolute values of the differences.
The absolute values are: 16, 17, 19, 23, 29, 31
Look at these carefully:
17, 19, 23, 29, 31 — these are five consecutive prime numbers!
But 16 is not a prime number (16 = 2 × 2 × 2 × 2).
Step 3: Identify the correct pattern.
The intended pattern is: alternate between adding and subtracting consecutive prime numbers — specifically 13, 17, 19, 23, 29, 31.
This means the first difference should be +13 (not +16), giving a first term of:
144 - 13 = 131
Step 4: Verify the corrected sequence starting at 131.
131 + 13 = 144 ✓
144 - 17 = 127 ✓
127 + 19 = 146 ✓
146 - 23 = 123 ✓
123 + 29 = 152 ✓
152 - 31 = 121 ✓
The corrected sequence is: 131, 144, 127, 146, 123, 152, 121
Conclusion: Every term from the 2nd onward fits the pattern perfectly. The first term, 128, breaks the rule — it should be 131. Therefore, 128 is the incorrect term in the sequence.
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