In the number series 8, 7, 11, 12, 14, 17, 17, 22, ( ... ), two interleaved arithmetic patterns are present. What is the next term that should replace the dots?

Introduction / Context:
This series question looks irregular at first glance, but a closer look reveals two arithmetic patterns interwoven together. The sequence alternates between two sub sequences, and the next term is determined by extending the pattern of the appropriate subsequence. Recognizing interleaved progressions is an important skill for solving many series questions in aptitude tests.

Given Data / Assumptions:

• The series given is 8, 7, 11, 12, 14, 17, 17, 22, ( ... ).
• We need to determine the missing next term.
• We suspect that odd indexed terms and even indexed terms may follow different arithmetic rules.
• The pattern is assumed to continue beyond the terms shown.

Concept / Approach:
Separate the sequence into two subsequences based on the positions of the terms. One subsequence consists of the terms at odd positions, and the other consists of the terms at even positions. Each subsequence is then inspected to see if it forms an arithmetic progression. Once these patterns are identified, the next term in the complete sequence can be obtained by continuing the appropriate subsequence.

Step-by-Step Solution:
Label the terms with their positions: position 1: 8, 2: 7, 3: 11, 4: 12, 5: 14, 6: 17, 7: 17, 8: 22. Take the odd position terms: positions 1, 3, 5, 7 give 8, 11, 14, 17. Observe that 8, 11, 14, 17 is an arithmetic progression with common difference 3. The next odd position term (position 9) will therefore be 17 + 3 = 20. Now check the even position terms: positions 2, 4, 6, 8 give 7, 12, 17, 22. The even position terms form an arithmetic progression with common difference 5. Thus position 10 would be 22 + 5 = 27, but the question only asks for the next term, which is position 9. Therefore, the next term to fill the blank in the given series is 20.

Verification / Alternative Check:
To confirm, list more terms using the discovered patterns. For odd positions, the terms are 8, 11, 14, 17, 20, ... For even positions, they are 7, 12, 17, 22, 27, ... Interleaving these gives 8 (1st), 7 (2nd), 11 (3rd), 12 (4th), 14 (5th), 17 (6th), 17 (7th), 22 (8th), 20 (9th), 27 (10th), and so on. This reproduces the original part of the series exactly and shows how the sequence continues, confirming that 20 is indeed the correct next term.

Why Other Options Are Wrong:

• Option 22: This is already used at position 8 as an even position term and does not fit the odd position pattern which increases by 3.
• Option 24: Would break the odd term arithmetic progression because the difference from 17 to 24 would be 7, not 3.
• Option 27: This is the expected value for position 10 (even position), not for position 9 which is odd.
• Option 19: Does not fit either the odd position arithmetic progression or the even position progression.

Common Pitfalls:
A typical mistake is to calculate simple differences between consecutive terms and look for a single pattern, which does not emerge clearly because the pattern is hidden in two subsequences. Another pitfall is to misidentify which positions are odd or even, leading to incorrect conclusions about the common differences. Properly labeling the positions and then separating the sequence is the safest approach.

Final Answer:
The missing next term in the series is 20.