Number series (find the wrong term): 1, 5, 9, 15, 25, 37, 49

Introduction / Context:
Some series hide two interleaved patterns. Recognizing the separation into odd-position and even-position terms is critical. Here, odd positions are perfect squares of odd integers, and even positions should be even squares plus one.

Given Data / Assumptions:

• Series: 1, 5, 9, 15, 25, 37, 49.
• Exactly one term is wrong.
• Consider splitting into two subsequences by position.

Concept / Approach:
Extract odd-index terms (1st, 3rd, 5th, 7th) and even-index terms (2nd, 4th, 6th). Check for recognizable patterns like perfect squares or small adjustments (+1 or −1) to squares.

Step-by-Step Solution:
Odd positions: 1, 9, 25, 49 → these are 1^2, 3^2, 5^2, 7^2 (perfect squares of consecutive odd numbers). Pattern is correct.Even positions: 5, 15, 37 → compare with even squares + 1: 2^2+1=5 (matches), 4^2+1=17 (expected), 6^2+1=37 (matches).Thus the fourth term 15 should be 17; it is the only mismatch.

Verification / Alternative check:
Corrected series: 1, 5, 9, 17, 25, 37, 49. Now both subsequences satisfy their respective rules perfectly (odd squares; even squares + 1).

Why Other Options Are Wrong:

• 9, 25, 37, 49 all align with the detected structure; replacing any of them breaks a consistent rule that the rest obey.

Common Pitfalls:

• Treating all steps uniformly and missing the interleaving of two simple, elegant patterns.
• Assuming differences must be constant or regularly increasing without considering positional rules.

Final Answer:
15