Answer :
To solve for the missing number in the sequence 142, 150, 123, 187, 62, ?, we need to identify a pattern or rule that relates these numbers.
First, let's analyze any potential patterns by considering differences between consecutive numbers:
Difference between 142 and 150: [tex]150 - 142 = 8[/tex]
Difference between 150 and 123: [tex]123 - 150 = -27[/tex]
Difference between 123 and 187: [tex]187 - 123 = 64[/tex]
Difference between 187 and 62: [tex]62 - 187 = -125[/tex]
These differences don't immediately suggest a simple arithmetic or geometric sequence. Another approach is to observe the sequence more abstractly for any hidden patterns associated with the numbers.
A different perspective might reveal that the differences themselves are noteworthy:
The differences are: 8, -27, 64, -125
These differences can be connected through a secondary sequence pattern: each difference is the cube of consecutive integers:
- [tex]2^3 = 8[/tex]
- [tex]-3^3 = -27[/tex]
- [tex]4^3 = 64[/tex]
- [tex]-5^3 = -125[/tex]
Following this pattern, the next step should be [tex]6^3 = 216[/tex]. Given the alternating sign pattern, this would involve subtracting:
[tex]62 + 216 = 278[/tex]
Thus, the missing number in the sequence is 278.
The complete sequence now becomes:
142, 150, 123, 187, 62, 278.
