Find the missing next term in the series: 8000, 1600, 320, 64, 12.8, ? Observe the repeated factor connecting consecutive terms.

Introduction / Context:In ratio-based series, a constant multiplier (or divisor) often links adjacent terms. Here the values sharply decrease in a uniform way.

Given Data / Assumptions:

• Series: 8000, 1600, 320, 64, 12.8, ?
• All transitions appear to be identical operations.

Concept / Approach:Check successive ratios: each term to the next should be the same constant.

Step-by-Step Solution:

Verification / Alternative check:Multiplying backward, 2.56 × 5 = 12.8 confirms the constant divisor.

Why Other Options Are Wrong:3.5 and 3.2 correspond to division by 3.657… or 4, not by 5; 2.98 is arbitrary here.

Common Pitfalls:Confusing alternating ratios; there is no alternation—just a fixed ÷5.

Final Answer:2.56.