Find the next two numbers that continue the alternating pattern. Sequence: 8, 12, 9, 13, 10, 14, 11, ____ , ____

Introduction / Context:
Here two simple progressions are interleaved: one affects odd-position terms and the other affects even-position terms. Recognizing the interleave is the key step.

Given Data / Assumptions:

• Series: 8, 12, 9, 13, 10, 14, 11, …
• We must supply the next two terms.

Concept / Approach:
Separate the series into odd and even indices; examine each subsequence independently.

Step-by-Step Solution:

Verification / Alternative check:
Write the two subsequences explicitly: odd = 8, 9, 10, 11, 12, … and even = 12, 13, 14, 15, … Interleaving them gives …, 11, 15, 12 which matches the derived pair.

Why Other Options Are Wrong:

• 14 11: Reverses the order and repeats existing values.
• 8 15 / 8 5: Return to earlier numbers breaks monotonic +1 growth.
• 15 19: Even term 15 is fine, but 19 ignores the +1 odd-step.

Common Pitfalls:
Continuing only one subsequence or mixing their orders. Always track position (odd/even) before extending.

Final Answer:
15 12