Question Details

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

Options

A

128

B

146

C

144

D

123

E

152

Show Answer

Correct Answer :

Option A

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

144+2=146

146+6=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:

121+2=123

123+4=127

127+6=133


Alternatively, looking at the step-by-step consecutive differences from term to term:

If the first term was 129 instead of 128:

129+15=144

Or observing the pattern of changes (+16, -17, +19, -23, +29, -31):

Working backward from 121:

7th term: 121
6th term: 152 (121+31=152)
5th term: 123 (152-29=123)
4th term: 146 (123+23=146)
3rd term: 127 (146-19=127)
2nd term: 144 (127+17=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:

144-15=129


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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