(81, 77, 69) — Identify the optioned triple that uses the same internal differences pattern as the given triple.

Introduction / Context:
Some triple analogies encode a sequence of signed differences between consecutive terms. For (81, 77, 69), the differences are −4 and −8 (i.e., 81−77 = 4, 77−69 = 8). The task is to choose the triple that follows the same “−4, then −8” pattern internally.

Given Data / Assumptions:

• (81, 77, 69) → differences: −4, −8.
• We seek an option with the same ordered pair of differences.

Concept / Approach:
Check each candidate: (56, 52, 44) has differences −4 and −8 (since 56−52 = 4, 52−44 = 8). The others do not mirror this exact ordered pair of differences.

Step-by-Step Solution:
1) Extract the ordered differences from the stem (−4, −8).2) Compute differences for each option.3) Select the triple that matches (−4, −8): (56, 52, 44).

Verification / Alternative check:
A quick mental subtraction confirms the pattern; only option (a) aligns exactly with the stem’s internal differences.

Why Other Options Are Wrong:
They either have different magnitudes or a different order of differences.

Common Pitfalls:
Accidentally matching unordered differences; here the order matters (first gap, then second gap).

Final Answer:
(56 , 52 , 44 )