Complete the series and evaluate A ÷ 36: 36, 216, 64.8, 388.8, A, 699.84, 209.952. Rule alternates ×6 and ×0.3 (i.e., ×3/10). Find A and then compute A ÷ 36.

Introduction / Context:This is a completion-and-evaluation series problem with a clear alternating multiplier pattern.

Given Data / Assumptions:

• Series: 36, 216, 64.8, 388.8, A, 699.84, 209.952.
• Rule: ×6, then ×0.3, repeating.

Concept / Approach:Apply the two-step alternation across the entire sequence, fill A, and finally compute the requested ratio.

Step-by-Step Solution:

Verification / Alternative check:Every adjacent ratio alternates between 6 and 0.3, confirming the correctness of A and the final division.

Why Other Options Are Wrong:0.324 and 6.139 are scale/rounding distractors; the exact arithmetic yields 3.24.

Common Pitfalls:Confusing ×0.3 with ÷3; note ×0.3 equals ÷(10/3), not ÷3.

Final Answer:3.24.