A number series is given with one term missing. Choose the correct alternative from the options that will complete the series: 200, 100, 50, 25, 12.5, 6.25, ?

Introduction / Context:
This question presents a decreasing number series involving decimals. The pattern appears to involve repeated halving of each term. Such series are useful for testing understanding of fractional operations and comfort with decimal arithmetic in reasoning problems.

Given Data / Assumptions:
Given series: 200, 100, 50, 25, 12.5, 6.25, ?We must determine the next term after 6.25.We assume that each term is related to the previous term by a consistent operation, likely division by 2.

Concept / Approach:
When numbers are steadily halved, the pattern is multiplicative with a ratio of 1 / 2 between consecutive terms. Recognizing this allows us to apply simple division repeatedly. The presence of decimals like 12.5 and 6.25 supports the idea that halving continues beyond whole numbers. We therefore check whether each term is exactly half of the previous one and then extend this process.

Step-by-Step Solution:
Step 1: Check 100 as half of 200: 200 / 2 = 100.Step 2: Check 50 as half of 100: 100 / 2 = 50.Step 3: Check 25 as half of 50: 50 / 2 = 25.Step 4: Check 12.5 as half of 25: 25 / 2 = 12.5.Step 5: Check 6.25 as half of 12.5: 12.5 / 2 = 6.25.Step 6: Continue the pattern by halving 6.25: 6.25 / 2 = 3.125.Step 7: Therefore, the missing term is 3.125.

Verification / Alternative check:
Write the fully extended series including the candidate term: 200, 100, 50, 25, 12.5, 6.25, 3.125. Each step is generated by dividing the previous term by 2. This steady halving is simple, consistent, and exactly matches all transitions in the series, confirming that 3.125 is the correct answer.

Why Other Options Are Wrong:
Option 2.125 does not equal 6.25 divided by 2 and would represent a ratio of approximately 0.34 instead of 0.5.Option 3.025 is not an exact half of 6.25 and suggests no clear fractionally consistent pattern.Option 2.025 is even further from half of 6.25 and completely breaks the halving rule that governs the series.

Common Pitfalls:
Some learners may be uncomfortable with decimals and therefore miscalculate the halving step after 6.25. Others might incorrectly round intermediate values, which can distort the pattern. It is important to perform exact halving, remembering that 6.25 is 6 and one quarter, so half of it is 3 and one eighth, which is 3.125 in decimal form.

Final Answer:
The missing number that continues the halving pattern is 3.125.