In the number series 13, 16, 11, 18, 9, 20, ?, select the missing term that continues the pattern.

Difficulty: Easy

Correct Answer: 7

Explanation:


Introduction / Context:

This question tests your ability to recognise patterns in number series, a common topic in reasoning and aptitude sections. The given series is 13, 16, 11, 18, 9, 20, ?, and you must find the rule governing the progression so that you can correctly identify the missing term. Often, such series use alternating patterns or combinations of addition and subtraction.


Given Data / Assumptions:

- Series: 13, 16, 11, 18, 9, 20, ? - Positions: 1st = 13, 2nd = 16, 3rd = 11, 4th = 18, 5th = 9, 6th = 20, 7th = ? - Options for the missing term: 3, 5, 6, 7.


Concept / Approach:

A useful technique for number series questions is to separate the terms into two alternating sub series: terms in odd positions and terms in even positions. Very often, each sub series follows its own simple pattern. Here, if you examine the numbers at odd and even positions separately, you will discover that one sub series decreases by 2 each time, while the other sub series increases by 2 each time. The missing term belongs to the decreasing sub series.


Step-by-Step Solution:

1. Extract the odd position terms: 1st = 13, 3rd = 11, 5th = 9, 7th = ? 2. Notice the pattern among these terms: 13 to 11 is a decrease of 2, and 11 to 9 is again a decrease of 2. 3. If this pattern continues, the next odd term should be 9 minus 2, which equals 7. 4. Now extract the even position terms: 2nd = 16, 4th = 18, 6th = 20. 5. Observe that 16 to 18 is an increase of 2, and 18 to 20 is another increase of 2. 6. This confirms that the series consists of two simple arithmetic progressions: one decreasing by 2 and one increasing by 2, interwoven. 7. Therefore, the missing 7th term in the decreasing odd position sub series must be 7.


Verification / Alternative check:

Write the series with the patterns marked: 13 (-2) 11 (-2) 9 (-2) 7 for the odd positions, and 16 (+2) 18 (+2) 20 for the even positions. Recombining them by alternating odd and even positions gives 13, 16, 11, 18, 9, 20, 7, which matches the original sequence with the missing term filled in. None of the other options, such as 3, 5, or 6, would preserve the simple minus two pattern in the odd term sub series.


Why Other Options Are Wrong:

3: Would make the odd position series 13, 11, 9, 3, which breaks the consistent minus two difference after the third term. 5: Would give 13, 11, 9, 5, where the last gap would be minus four, again breaking the pattern. 6: Does not fit a simple minus two or minus four pattern from 9, and creates inconsistency between differences.


Common Pitfalls:

Many students initially try to find a single rule that connects every term to the next one, such as adding or subtracting alternating numbers, and become confused. The smarter approach is to split the series based on position parity when simple direct rules do not appear. Recognising that many exam series are built from two interlaced arithmetic or geometric progressions can save a lot of time and reduce errors.


Final Answer:

The missing number in the series is 7.

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