Discussion
Look at the gaps between successive letters rather than at the letters themselves, and complete the sequence.
B, C, E, H, L, ?
Answer: B
Correct answer: Q
The differences increase by one at every step: B to C is +1, C to E is +2, E to H is +3, H to L is +4, so the next must be +5. Five beyond L(12) is position 17, giving Q. Note that the terms are at positions 2, 3, 5, 8, 12, 17 - each is the previous plus the running count. P at 16 would follow from repeating the +4 step instead of increasing it. The running total of the gaps is 1, 3, 6, 10, 15 - the triangular numbers - so the position of the nth term is always the starting position plus a triangular number.
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