In this alternating number series question, find the next term in the sequence: 11, 5.5, 10, 6.5, 9, ?

Introduction / Context:
This problem illustrates a classic alternating number series used in aptitude exams. The sequence 11, 5.5, 10, 6.5, 9, ? interleaves two simpler subseries. Identifying these hidden subseries is the key to quickly and accurately determining the missing term.

Given Data / Assumptions:

• Full series: 11, 5.5, 10, 6.5, 9, ?
• The series alternates between two patterns, one on odd positions and one on even positions.
• Exactly one value correctly continues both underlying patterns.

Concept / Approach:
When a sequence seems to move up and down without a simple rule, it often consists of two interleaved sequences. We split the terms into two groups: those in odd positions and those in even positions. Each group is then analyzed separately for a simple arithmetic pattern such as a fixed increase or decrease.

Step-by-Step Solution:
Step 1: Separate the sequence into odd and even positions.Odd positions (1, 3, 5): 11, 10, 9.Even positions (2, 4, 6): 5.5, 6.5, ?.Step 2: Analyze the odd-position series.11 to 10: decrease by 1.10 to 9: decrease by 1.Thus, odd-position terms follow: 11, 10, 9, 8, ... (subtract 1 each time).Step 3: Analyze the even-position series.5.5 to 6.5: increase by 1.Therefore, the next even-position term should be 6.5 + 1 = 7.5.Step 4: Place this result in the original sequence as the sixth term.The completed sequence becomes 11, 5.5, 10, 6.5, 9, 7.5.

Verification / Alternative check:
Rechecking both subseries confirms the logic. The odd-position series is a simple decreasing sequence with difference minus 1 each time. The even-position series is a simple increasing sequence with difference plus 1 each time. Since 7.5 satisfies the even-position pattern without disturbing the odd-position pattern, it is the unique correct answer.

Why Other Options Are Wrong:
6.5: Repeating 6.5 would break the clean increasing pattern of the even positions.
8.5: This would introduce an increase of 2 from 6.5, which does not match the earlier step of +1.
10.5: This value is too large and does not fit either the odd or even subseries pattern.

Common Pitfalls:
Many learners attempt to find a single rule relating consecutive terms and become confused by the apparent irregularity. The key is to recognize that some sequences interleave two simpler progressions. Always try splitting into odd and even positions when the series seems to bounce up and down without a simple linear pattern.

Final Answer:
The next term in the series is 7.5.