Number series with a periodic constant term – find the next two numbers. Sequence: 3, 5, 35, 10, 12, 35, 17, ____ , ____

Introduction / Context:
This series alternates two behaviors: an increasing subsequence and a fixed repeating value that appears at regular positions. Recognizing the period of the fixed term is key.

Given Data / Assumptions:

• Given: 3, 5, 35, 10, 12, 35, 17, …
• Find the next two terms.

Concept / Approach:
Note that every third term is 35, while the other terms form their own +2 progression across non-multiple-of-3 indices.

Step-by-Step Solution:

Verification / Alternative check:
Check back: positions 1,2,4,5,7 follow +2 steps, and 3,6,9 are constant at 35. The pattern is fully consistent.

Why Other Options Are Wrong:

• 22 35 / 19 24: Misapply +3 or create a non-existent jump.
• 35 19: Reverses the order; 35 must be the 9th term, not 8th.
• 22 24: Ignores the required 35 at position 9.

Common Pitfalls:
Forgetting to check positional periodicity; not all patterns are simple differences—some embed a repeating constant at fixed intervals.

Final Answer:
19 35