The first letters are A(1), C(3), E(5) and G(7), increasing by 2 each time. The second letters are D(4), F(6), H(8) and J(10), also increasing by 2. The next first letter is 7 + 2 = 9 (I) and the next second letter is 10 + 2 = 12 (L), forming IL. Thus IL uniquely maintains the +2 increment for both positions.
Option A:
Option A is correct because both I and L are exactly two positions ahead of G and J respectively. It preserves the parallel arithmetic progression in both components of the pair. This consistent step size is what defines the pattern, making IL the valid next term.
Option B:
Option B, IK, uses I correctly as the first letter but keeps K as the second. K is only one step ahead of J instead of two. This breaks the constant +2 difference in the second position, so IK cannot be correct.
Option C:
Option C, JL, advances the first letter by three positions from G to J while keeping the second letter L plausible. However, the first-letter sequence clearly uses steps of 2, not 3. This mismatch in the first position means JL does not follow the series rule.
Option D:
Option D, HM, shifts the first letter from G to H, which is only a single step, and moves the second letter too far to M. Both positions now violate the established +2 pattern. Consequently, HM cannot be accepted as the next term.
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