Find the wrong number in the sequence 125, 127, 130, 135, 142, 153, 165
2011
Find the wrong number in the sequence
125, 127, 130, 135, 142, 153, 165
Answer: D. 165 — CONCEPTA number-series rule is identified by comparing successive terms. When the differences follow a known ordered pattern, each next term is obtained by…
- A.
130
- B.
142
- C.
153
- D.
165
Attempted by 5 students.
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Correct answer: D
CONCEPT
A number-series rule is identified by comparing successive terms. When the differences follow a known ordered pattern, each next term is obtained by adding the next value in that difference pattern.
APPLICATION
The successive differences are 127 − 125 = 2, 130 − 127 = 3, 135 − 130 = 5, 142 − 135 = 7, 153 − 142 = 11, and 165 − 153 = 12.
The intended differences are consecutive prime numbers: 2, 3, 5, 7, 11, 13.
After 153, the next term should therefore be 153 + 13 = 166, not 165.
CROSS-CHECK
Starting from 125 and adding 2, 3, 5, 7, 11, and 13 gives 127, 130, 135, 142, 153, and 166. Thus 165 is the wrong number in the displayed sequence.