In each series, one term is wrong. You have to find the wrong term of the…

Concept

In a wrong-number-series item, every term is produced from the one before it by a single governing rule. Here the rule alternates between adding a perfect cube and a perfect square: step 1 adds 1 cubed, step 2 adds 2 squared, step 3 adds 3 cubed, step 4 adds 4 squared, step 5 adds 5 cubed, and step 6 adds 6 squared. Exactly one given term breaks this alternating cube-square addition rule, and that broken term is the answer.

How to apply it

1. Step 1: 7 + 1 cubed (1) = 8, which matches the given second term.

2. Step 2: 8 + 2 squared (4) = 12, but the given third term is 16 -- it does not match this expected 12.

3. Step 3: continuing the rule from the expected 12: 12 + 3 cubed (27) = 39, which matches the given fourth term.

4. Step 4: 39 + 4 squared (16) = 55, which matches the given fifth term.

5. Step 5: 55 + 5 cubed (125) = 180, which matches the given sixth term.

6. Step 6: 180 + 6 squared (36) = 216, which matches the given seventh (last) term.

Cross-check

Every later term (39, 55, 180, 216) lines up exactly once the third term is treated as 12 instead of 16, and the same alternating cube-square rule accounts for all six steps without a single exception elsewhere. This confirms the rule is the series' single governing pattern and that the third term is the one place it fails.

So the wrong term in the series is 16.