Patterned Series — Alternating Odd Increments and Decrements Find the missing term: 8, 9, 8, 7, 10, 9, 6, 11, 10, ?, 12

Introduction / Context:This series weaves two alternating move types: small decrements and larger positive jumps that grow by odd numbers. Recognizing the repeating pattern of +odd and −odd steps unlocks the missing term quickly.

Given Data / Assumptions:

• Series: 8, 9, 8, 7, 10, 9, 6, 11, 10, ?, 12
• Observe alternating local increases and decreases.

Concept / Approach:Track the changes between successive terms. You will see a repeating structure: small −1 or larger −odd, followed by an increasing +odd (3, 5, 7, ...). The missing value sits just before the final +7 step that reaches 12.

Step-by-Step Solution:8 → 9: +19 → 8: −18 → 7: −17 → 10: +310 → 9: −19 → 6: −36 → 11: +511 → 10: −110 → ?: −5? → 12: +7Solving back: since ? → 12 is +7, ? = 12 − 7 = 5

Verification / Alternative check:The negative steps grow as −1, −1, −3, −1, −5 and the positive jumps grow as +3, +5, +7. This consistent alternation confirms 5 before the final +7.

Why Other Options Are Wrong:

• 7, 8, 11: None allow a +7 step to reach 12 while preserving the established −5 decrement before it.

Common Pitfalls:Looking for two independent interleaved sequences only by position. Here, direct consecutive differences reveal the intended pattern more transparently.

Final Answer:5