Number Series — Find the Wrong Term (Alternating Subsequence Insight) Identify the incorrect number in: 89, 78, 86, 80, 85, 82, 83.

Introduction / Context:Some wrong-number series are best solved by splitting into two interleaved subsequences (odd and even positions). When each subsequence follows its own steady rule, the lone mismatch becomes visible.

Given Data / Assumptions:

• Full sequence: 89, 78, 86, 80, 85, 82, 83
• Positions: 1-based indexing helps identify alternating patterns.
• Exactly one term is wrong.

Concept / Approach:Separate the sequence by position parity.Odd positions (1, 3, 5, 7): 89, 86, 85, 83Even positions (2, 4, 6): 78, 80, 82The even-position subsequence clearly increases by +2 each time (78 → 80 → 82). The odd-position subsequence should ideally form a simple steady decrease, typically by 2 steps to mirror even regularity (89 → 87 → 85 → 83).

Step-by-Step Solution:Expected odd subsequence: 89, 87, 85, 83Given odd subsequence: 89, 86, 85, 83Mismatch at position 3 (overall sequence index): 86 should have been 87.

Verification / Alternative check:If 86 is replaced by 87, both subsequences become perfectly regular: odd positions decrease by 2 each step and even positions increase by 2 each step.

Why Other Options Are Wrong:

• 78, 82, 83: These fit the +2 even subsequence or the −2 odd subsequence properly and therefore are not erroneous.

Common Pitfalls:Examining only consecutive differences across the whole list can obscure a clean interleaving structure. Always test odd/even positions when patterns seem jagged.

Final Answer:86