Multiple choice

Find the missing term in the following sequence. $177, 170, 159, 146, ?, 110$.

  1. $132$
  2. $106$
  3. $129$
  4. $127$

  5. None of these
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C Correct answer
Explanation

Differences: 177-170=7, 170-159=11, 159-146=13. The differences are prime numbers (7, 11, 13). The next prime is 17. 146 - 17 = 129. Check: 129 - 19 = 110. Correct.

AI explanation

Subtract consecutive terms to find the differences. The difference between 177 and 170 is -7, between 170 and 159 is -11, and between 159 and 146 is -13. The differences form a sequence of consecutive prime numbers negated (-7, -11, -13), so the next difference is -17. Subtracting 17 from 146 gives 129, which correctly precedes 110 when subtracting the next prime number, 19. The result is 129.

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