A series of units of length is given with one term missing. Choose the correct alternative from the options that will complete the series. Inch, Decameter, Foot, ?

Introduction / Context:
Reasoning questions that mix metric and imperial units test whether candidates can recognise patterns beyond simple numerical progressions. Here, the series lists different units of length from two systems. To decide the missing term, we must identify the underlying logic rather than attempting to convert all units into numerical values alone. The pattern often alternates between systems or between smaller and larger units in a structured way.

Given Data / Assumptions:

• Given series: Inch, Decameter, Foot, ?
• Inch and Foot are common imperial units of length.
• Decameter and Meter are standard metric units based on powers of ten.
• The question likely uses a conceptual pattern, for example alternating between imperial and metric units.

Concept / Approach:
Inch and Foot belong to the same family of units, while Decameter belongs to the metric system. The series starts with an imperial unit (Inch), then switches to a metric unit (Decameter), then returns to an imperial unit (Foot). The most natural and simple continuation of this pattern is to follow Foot with a metric unit of length. Among the options, Meter is the fundamental and most common metric unit that pairs meaningfully with Inch and Foot in everyday comparisons.

Step-by-Step Solution:
Step 1: Note the system for each unit: Inch (imperial), Decameter (metric), Foot (imperial). Step 2: Observe that the pattern alternates between imperial and metric systems: imperial, metric, imperial, so the next term should logically be a metric unit. Step 3: Among the metric options, Decimeter, Millimeter, Centimeter, Meter, and Kilometer are all valid metric units, but Meter is the base unit most closely associated with common comparisons to inches and feet. Step 4: Therefore, Meter is the most appropriate and expected choice to complete the alternating pattern, giving the sequence: Inch (imperial), Decameter (metric), Foot (imperial), Meter (metric).

Verification / Alternative check:
Another way to check is to see how typical exam setters choose familiar pairs. Inch naturally pairs with centimeter or meter, and foot commonly pairs with meter when explaining conversions. Using Meter after Foot keeps the series familiar and educational. The other metric units such as millimeter or kilometer either represent extreme sizes or are less commonly paired directly with both inch and foot in simple reasoning sequences. This supports Meter as the most reasonable and exam friendly continuation.

Why Other Options Are Wrong:
Decimeter, Millimeter, and Centimeter are all very small metric units compared to Decameter, which is large, and they would create an inconsistent sequence of magnitudes with no clear pattern. Kilometer is a large unit used for long distances and again does not form a simple pairing with Foot in typical conversion examples. These options do not highlight the neat alternation between imperial and metric systems and do not provide the same natural sense of balance that the pair Foot and Meter gives.

Common Pitfalls:
A common mistake is to look for increasing or decreasing numerical size strictly, which is difficult because Inch, Foot, Decameter, and the options do not form a simple arithmetic or geometric progression. Another error is to choose Decimeter or Centimeter simply because they seem similar in spelling to Decameter and Centimeter, without checking whether that leads to a clear and logical pattern. For exam questions, the simplest and most educational pattern, such as alternating between imperial and metric units with familiar pairs, is usually the intended one.

Final Answer:
Following the alternating pattern between imperial and metric units, the sequence is best completed by the metric base unit Meter after Foot.