Number series (find the wrong term): 64, 71, 80, 91, 104, 119, 135, 155 One entry breaks the odd-increment pattern. Identify the wrong term and justify your reasoning.

Introduction / Context:
Series formed by adding successive odd numbers are very common. Here, the increments appear to grow by 2 each time. We must detect the single place where the increment is not the expected odd step.

Given Data / Assumptions:

• Series: 64, 71, 80, 91, 104, 119, 135, 155
• Exactly one term is wrong.

Concept / Approach:
Compute the differences: 71−64 = 7, 80−71 = 9, 91−80 = 11, 104−91 = 13, 119−104 = 15, 135−119 = 16, 155−135 = 20. The intended pattern is adding consecutive odd numbers: +7, +9, +11, +13, +15, +17, +19.

Step-by-Step Solution:
Up to 119, the increments are 7, 9, 11, 13, 15 ✔Next should be +17, so 119 + 17 = 136, but the series shows 135 ✖Finally, the next increment should be +19, and from the corrected 136, 136 + 19 = 155 ✔Thus, only 135 is inconsistent; it should have been 136.

Verification / Alternative check:
Replace 135 with 136; the full list of differences becomes +7, +9, +11, +13, +15, +17, +19, a perfect run of consecutive odd numbers.

Why Other Options Are Wrong:

• 71, 80, 104, 119: They fit the expected odd increments sequence.
• 135: Breaks the odd-number increment pattern by using +16 instead of +17.

Common Pitfalls:
Overlooking a single off-by-one error among many correct odd increments. Always compute all consecutive differences.

Final Answer:
135