What is X in the sequence 1, 3, 6, 11, 18, X, 42?

What is X in the sequence 1, 3, 6, 11, 18, X, 42?
  1. 26
  2. 27
  3. 29
  4. 30

Solution

The differences between consecutive terms are: $3-1=2$, $6-3=3$, $11-6=5$, $18-11=7$, ?, $42-X$. The differences 2, 3, 5, 7 are successive primes, so the next difference is 11: $X = 18+11 = 29$. Check: next difference 13 gives $29+13 = 42$, consistent. Hence X = 29.

Asked in: CSAT 2025

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