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142, 150, 123, 187, 62, ?

Select the missing number.

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:

  1. Difference between 142 and 150: [tex]150 - 142 = 8[/tex]

  2. Difference between 150 and 123: [tex]123 - 150 = -27[/tex]

  3. Difference between 123 and 187: [tex]187 - 123 = 64[/tex]

  4. 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.

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