The missing letters in the given letter series are: BCE, CDG, DEI, ______, FGM

In a series built from fixed-length letter blocks, each position across the blocks (the 1st letters, the 2nd letters, the 3rd letters) forms its own independent sub-series. Convert every letter to its alphabet position (A=1, B=2, ..., Z=26); the resulting numbers in each column usually follow a simple arithmetic rule — a constant common difference, or a common difference that itself grows by a fixed step from block to block.

Application: Write the alphabet positions of every block.

1. 1st-letter column: 2, 3, 4, ?, 6 — each term rises by exactly 1, so the missing value is 5, which is E.

2. 2nd-letter column: 3, 4, 5, ?, 7 — each term rises by exactly 1, so the missing value is 6, which is F.

3. 3rd-letter column: 5, 7, 9, ?, 13 — each term rises by exactly 2, so the missing value is 11, which is K.

4. Combining the three columns gives the missing block: E, F, K.

Cross-check: Look instead at the two internal jumps inside each block (1st→2nd letter, then 2nd→3rd letter). Block BCE jumps by 1 then 2; CDG jumps by 1 then 3; DEI jumps by 1 then 4; FGM jumps by 1 then 6. The first internal jump stays fixed while the second one climbs 2, 3, 4, ?, 6 — so the missing block's second jump is 5. Starting the missing block at E, the first jump of 1 gives F, and the second jump of 5 from F gives K — the same E, F, K found from the column method, confirming it independently.

So the missing letters are EFK.