Difficulty: Easy
Correct Answer: 39
Explanation:
Introduction / Context:
This number series problem involves an alternating pattern. The sequence provided is 6, 8, 17, 19, 28, 30, ?. The task is to discover the rule that generates each term and then use it to find the missing number. Many exam questions use two intertwined patterns, so recognising such alternation is a key reasoning skill.
Given Data / Assumptions:
Given series: 6, 8, 17, 19, 28, 30, ?
The missing term comes after 30.
There may be two related subsequences interwoven in alternate positions.
Exactly one option will match a consistent pattern that extends the series.
Concept / Approach:
A good approach here is to split the series into two subsequences: terms at odd positions and terms at even positions. Often, one subsequence follows a particular rule (for example, adding a constant), while the other follows a similar or slightly different rule. This method is especially useful when the overall series seems to jump irregularly.
Step-by-Step Solution:
Write the terms with their positions: 1st: 6, 2nd: 8, 3rd: 17, 4th: 19, 5th: 28, 6th: 30, 7th: ?.
Odd-position terms: 6 (1st), 17 (3rd), 28 (5th), ? (7th).
Even-position terms: 8 (2nd), 19 (4th), 30 (6th).
For odd positions: 6 to 17 is +11, 17 to 28 is +11, so the next should be 28 + 11 = 39.
For even positions: 8 to 19 is +11, 19 to 30 is also +11, confirming the same rule.
Thus, both subsequences increase by 11, and the missing term is 39.
Verification / Alternative check:
Combine the subsequences back: 6, 8, 17, 19, 28, 30, 39. Odd-position terms follow 6, 17, 28, 39 with a constant difference of 11; even-position terms follow 8, 19, 30, also with difference 11. This symmetrical structure confirms that the discovered rule is strong and consistent, leaving no doubt that 39 is the only suitable answer.
Why Other Options Are Wrong:
Option A: 32 does not follow the +11 rule from 28 and would break the odd-position subsequence pattern.
Option B: 37 uses +9 instead of +11, which is inconsistent with all earlier jumps of 11.
Option C: 38 uses +10, again breaking the uniform difference of 11.
Option E: 35 is also not at a distance of 11 from 28 and does not match the observed structure.
Common Pitfalls:
Some candidates may only look at consecutive differences (2, 9, 2, 9, 2, ?) and fail to realise that two sequences are interwoven. Recognising alternating patterns is very important for solving a wide variety of number series questions quickly. Another pitfall is to assume a single arithmetic or geometric progression without exploring the possibility of multiple embedded patterns.
Final Answer:
The term that correctly completes the series is 39, so the correct option is 39.
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