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 option is 128.
To identify the incorrect term in the sequence, let us analyze the pattern of differences between consecutive numbers in the sequence:
128, 144, 127, 146, 123, 152, 121
Let us look at the operations between consecutive terms starting from the right or analyzing the alternate pattern:
Notice the alternate terms forming two sub-sequences:
First alternate sequence (2nd, 4th, 6th terms):
144, 146, 152
Second alternate sequence (1st, 3rd, 5th, 7th terms):
128, 127, 123, 121
Let us check the differences going backward from the last term, 121:
Alternatively, looking at the step-by-step consecutive differences from term to term:
If the first term was 129 instead of 128:
Or observing the pattern of changes (+16, -17, +19, -23, +29, -31):
Working backward from 121:
7th term: 121
6th term: 152 ()
5th term: 123 ()
4th term: 146 ()
3rd term: 127 ()
2nd term: 144 ()
The sequence of prime numbers added/subtracted alternately is: 13, 17, 19, 23, 29, 31.
To get the 2nd term (144) using the prime difference of 15/13 pattern:
Therefore, the first term should be 129 instead of 128 to maintain the mathematical rule. Thus, 128 is the incorrect term in the sequence.
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