Number series (cyclic adjustments: +10, then +a, then −a+10 with a reducing by 8) Sequence: 16 26 56 36 46 68 56 … Choose the next two numbers that fit the evolving increment cycle.

Introduction / Context:
Not all series are simple arithmetic or geometric progressions. Some use a repeating three-step cycle with changing magnitudes. Recognizing the higher-level cycle and how its parameters evolve is essential.

Given Data / Assumptions:

• Sequence: 16, 26, 56, 36, 46, 68, 56, …
• Observed increments: +10, +30, −20, +10, +22, −12, …

Concept / Approach:
Group the changes into triplets. The pattern is: add 10, then add a, then subtract (a − 10). The parameter a decreases by 8 each cycle: first a = 30, next a = 22, next a = 14, and so on.

Step-by-Step Solution:

Verification / Alternative check:
Continuing would give the third step of this cycle as −4 (14 − 10), validating the evolving pattern.

Why Other Options Are Wrong:

• 80 66 / 64 82 / 78 68 / 66 82: They break the established three-step cycle or use incorrect values for the evolving parameter a.

Common Pitfalls:
Assuming a single fixed difference or ratio without examining the sequence of increments themselves.

Final Answer:
66 80