Find the odd number out in the series: 1050, 510, 242, 106, 46, 16, 3

Concept: A 'find the odd number out' series question generates each term from the one before it by a single consistent rule. State that rule explicitly, verify it holds for every consecutive pair of given terms, and the one pair where it fails identifies the odd (incorrect) term.

Application:

1. Subtract 30 from 1050 and halve the result: (1050 − 30) ÷ 2 = 510.

2. Subtract 26 from 510 and halve the result: (510 − 26) ÷ 2 = 242.

3. Subtract 22 from 242 and halve the result: (242 − 22) ÷ 2 = 110 — but the series lists 106 instead of 110.

4. Continuing forward from the expected value 110: (110 − 18) ÷ 2 = 46.

5. (46 − 14) ÷ 2 = 16.

6. (16 − 10) ÷ 2 = 3.

Cross-check: The numbers subtracted at each step — 30, 26, 22, 18, 14, 10 — themselves decrease by a constant 4, confirming the rule independently. Recomputing the third step directly, 242 − 22 = 220, and 220 ÷ 2 = 110, confirms 106 is inconsistent with the sequence.

Therefore, 106 is the odd number out; it should be 110 to keep the pattern consistent.