Identify the wrong term in a square-number increment pattern: 1, 2, 6, 15, 31, 56, 91

Introduction / Context:
This series is formed by adding consecutive perfect squares to build each next term. A single off-by-one near the end reveals the incorrect entry.

Given Data / Assumptions:

• Series: 1, 2, 6, 15, 31, 56, 91.
• Intended increments: +1^2, +2^2, +3^2, +4^2, +5^2, +6^2.

Concept / Approach:
Compute successive differences and see whether they match 1, 4, 9, 16, 25, 36. The first five steps align; the last does not, exposing the wrong term.

Step-by-Step Solution:
2 − 1 = 1 (1^2)6 − 2 = 4 (2^2)15 − 6 = 9 (3^2)31 − 15 = 16 (4^2)56 − 31 = 25 (5^2)Next should be +36 ⇒ 56 + 36 = 92 (but given: 91)

Verification / Alternative check:
Correcting 91 to 92 reestablishes the perfect-squares increment ladder. No other simple pattern explains all earlier steps as cleanly.

Why Other Options Are Wrong:

• 31 / 56 / 15 each sits exactly at the right cumulative square-sum.

Common Pitfalls:

• Misreading late-series arithmetic by 1; always check the exact square increment expected.

Final Answer:
91