Find the next term in the number series 2A11, 4D13, 12G17, 48J23, ________ .

Concept

An alpha-numeric series interleaves two or more independent sequences inside a single term. The method is fixed: split every term at the same positions, follow each component across the whole series as its own sequence, name the rule that governs that component, and only then rebuild the missing term from the separate rules.

The component rules met most often are a multiplier that itself steps up (multiply by 2, then 3, then 4, and so on), a constant shift in alphabet position, and a difference that itself grows in arithmetic progression.

Application

Every term here has the shape [number][letter][number], so the four given terms split as 2 | A | 11, 4 | D | 13, 12 | G | 17 and 48 | J | 23.

1. Prefix numbers: 2 to 4 is a multiplication by 2, 4 to 12 is a multiplication by 3, and 12 to 48 is a multiplication by 4. The multiplier itself rises by 1 at each step, so the next multiplier is 5, giving 48 × 5 = 240.

2. Middle letters: A, D, G and J occupy alphabet positions 1, 4, 7 and 10, a constant step of +3. The next position is 10 + 3 = 13, which is the letter M.

3. Suffix numbers: 11 to 13 is +2, 13 to 17 is +4, and 17 to 23 is +6. The difference itself grows by 2 each time, so the next difference is +8, giving 23 + 8 = 31.

4. Reassembling the three components in their original order gives the prefix 240, the letter M and the suffix 31, that is, 240M31.

Cross-check

Rebuild each component forward from the first term using the rule found for it, and check that the reconstruction reproduces every term that was actually given.

All three reconstructions reproduce the four given terms exactly, so the fifth term of the series is 240M31.