What is the next term of the following sequence K , A , J , B , I , C , H , (_…

Concept

An alternating (interleaved) letter series is really two independent series woven together: the terms at the odd positions form one sequence, and the terms at the even positions form another. To extend the series, treat each position group separately - track how each group's letters change from one term to the next within that group alone, then continue that group's own rule forward.

Application

1. Separate the two given interleaved runs by position: the odd-position terms are K, J, I, H (the 1st, 3rd, 5th, and 7th terms), and the even-position terms are A, B, C (the 2nd, 4th, and 6th terms).

2. Find each run's own step rule: the odd-position run moves backward through the alphabet by one letter each time (K -> J -> I -> H), and the even-position run moves forward through the alphabet by one letter each time (A -> B -> C).

3. Continue the even-position run one more step past C to get the 8th term, then continue the odd-position run one more step past H to get the 9th term, then continue the even-position run one more step further to get the 10th term.

4. Reading these three new terms in the order they occur gives the letters that belong in the blank: D, G, E.

Cross-check

Rebuilding the full ten-term sequence with these three new letters keeps both runs internally consistent - the odd-position letters (K, J, I, H, G) still form one unbroken backward alphabet run, and the even-position letters (A, B, C, D, E) still form one unbroken forward alphabet run, with no repeated or skipped letters in either run.

So the 8th, 9th, and 10th terms are D, G, and E - the missing group is D, G, E.