In this simple number series question, one term is missing. Observe the pattern in 10, 12, 14, 16, 18, ? and choose the correct alternative that completes the series.

Difficulty: Easy

Correct Answer: 20

Explanation:


Introduction / Context:
This is a straightforward number series problem. The given sequence is 10, 12, 14, 16, 18, ?. The aim is to identify the pattern connecting the terms and then determine the missing next value. Such questions commonly test quick recognition of basic arithmetic progressions in competitive exams and placement tests.


Given Data / Assumptions:
Series: 10, 12, 14, 16, 18, ?
One term is missing at the end of the series.
The sequence appears to be increasing steadily by a constant amount.
Exactly one option will continue this simple pattern correctly.


Concept / Approach:
For small, regularly increasing series, we first check for an arithmetic progression. That means each term differs from the previous one by a fixed quantity. If the difference between consecutive terms is the same, we can easily extend the sequence by adding that common difference to the last known term.


Step-by-Step Solution:
Compute the differences: 12 - 10 = 2. Next: 14 - 12 = 2. Next: 16 - 14 = 2. Next: 18 - 16 = 2. The common difference between consecutive terms is 2 throughout. To find the missing term, add 2 to the last known term: 18 + 2 = 20. Therefore, the missing number is 20.


Verification / Alternative check:
Rewriting the series with the missing term included: 10, 12, 14, 16, 18, 20. This is a clear arithmetic progression starting at 10 with a common difference of 2. None of the other options gives such a smooth pattern. The sequence also corresponds to consecutive even numbers from 10 to 20, which further confirms the correctness of the answer.


Why Other Options Are Wrong:
Option A: 22 would correspond to 18 + 4, which breaks the constant difference of 2.
Option B: 24 also does not follow the +2 rule and would skip several intermediate terms.
Option D: 26 is even further away and clearly inconsistent with the basic progression.
Option E: 28 is not the immediate successor in the pattern and would represent multiple missed steps.


Common Pitfalls:
This problem is simple, but under exam pressure candidates may overthink and search for a complicated rule. Another possible pitfall is misreading the final term and adding an incorrect difference. Always confirm that the same difference appears consistently between all consecutive terms before making a conclusion.


Final Answer:
The number that continues the pattern of adding 2 each time is 20, so the correct option is 20.

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