In the following question, select the missing number from the given series: 192, 186, 180, 174, ?, 162

Introduction / Context:
This problem presents a simple decreasing arithmetic series. Each term is obtained by subtracting the same number from the previous term. Quick recognition of this constant difference is important in many competitive exams. The series given is 192, 186, 180, 174, ?, 162.

Given Data / Assumptions:
- Terms: 192, 186, 180, 174, ?, 162.- One term between 174 and 162 is missing.- The values decrease steadily with no abrupt changes.- A constant negative difference is the most likely pattern.

Concept / Approach:
We compute differences between consecutive known terms. If the same difference appears repeatedly, we can apply it to find the missing term. This is the standard approach for arithmetic sequences, which are among the simplest types of number series.

Step-by-Step Solution:
- From 192 to 186: 186 - 192 = -6.- From 186 to 180: 180 - 186 = -6.- From 180 to 174: 174 - 180 = -6.- Thus the series decreases by 6 at each step.- To find the next term after 174, subtract 6: 174 - 6 = 168.- Check the last term: 168 - 6 = 162, which matches the series.

Verification / Alternative check:
- With 168 inserted, the full sequence is 192, 186, 180, 174, 168, 162.- Every transition subtracts exactly 6, confirming an arithmetic series with common difference -6.- No other candidate preserves this constant step throughout the series.

Why Other Options Are Wrong:
- 166 and 170 would result in differences that are not equal to -6 at every step.- 164 and 172 either produce too large or too small a gap to lead on to 162 with the same difference.- Only 168 fits smoothly into the pattern of subtracting 6 each time.

Common Pitfalls:
- Miscalculations in subtraction can cause the common difference to be misread.- Some candidates might guess based purely on approximate closeness to 174 or 162 without checking all steps.- Overcomplicating the sequence with imagined higher order rules is unnecessary for such a simple arithmetic series.

Final Answer:
The series subtracts 6 at each step, so the missing term is 168.