A series is given with one term missing. Choose the correct alternative from the given options that will complete the series: 72, 56, 42, 30, 20, ?

Introduction / Context:
This series decreases in steps that themselves follow a simple pattern of even numbers. Many exam questions use decreasing sequences where the subtracted values form an arithmetic progression. The given series is 72, 56, 42, 30, 20, ?, and we must find the missing final term.

Given Data / Assumptions:
- Terms: 72, 56, 42, 30, 20, ?- Only the last term is missing.- The sequence is strictly decreasing.- The subtracted values appear to be consecutive even numbers.

Concept / Approach:
The first step is to compute the differences between consecutive terms. If these differences follow a simple pattern, such as -16, -14, -12, -10, -8, we can use that pattern to determine the missing number. This is a classic use of first differences in arithmetic series problems.

Step-by-Step Solution:
- From 72 to 56: 56 - 72 = -16.- From 56 to 42: 42 - 56 = -14.- From 42 to 30: 30 - 42 = -12.- From 30 to 20: 20 - 30 = -10.- The absolute values of the differences are 16, 14, 12, 10, which decrease by 2 each time.- Therefore, the next difference should be -8.- So the missing term is 20 - 8 = 12.

Verification / Alternative check:
- With 12 as the last term, the full sequence of differences is -16, -14, -12, -10, -8.- These differences form a clear arithmetic progression of even numbers decreasing by 2 each time.- No alternative value maintains this neat progression of step sizes.

Why Other Options Are Wrong:
- 22 and 20 would actually increase or keep the value constant relative to 20, which contradicts the decreasing trend.- 62 does not fit anywhere nearby and would produce a difference inconsistent with the pattern of even decrements.- Only 12 preserves both the direction and the structure of the decreasing differences.

Common Pitfalls:
- Forgetting to consider the sign of the differences and focusing only on magnitudes may cause confusion.- Some candidates attempt to find a multiplicative pattern where a simple subtraction pattern is sufficient.- Miscomputing one difference, such as reading -14 as -15, can hide the clear even number sequence.

Final Answer:
The differences decrease as -16, -14, -12, -10, -8, so the missing term is 12.