In the following number series only one number is wrong. Find out the wrong…

Concept: In a wrong-number-in-series question, every term is obtained from the previous term by one single rule (here, multiply by a constant and add a value that itself increases by 1 each step); the term that violates this rule when compared with its neighbours is the anomaly to find.

Series: 14, 22, 34.5, 55.5, 87.25, 135.875, 209.8125

1. 14 x 1.5 + 1 = 22, which matches the second term, so the first transformation checks out.

2. 22 x 1.5 + 2 = 35, but the series shows 34.5 in that position — this is where the pattern breaks.

3. Continuing the rule from the corrected value 35: 35 x 1.5 + 3 = 55.5, which matches the fourth term.

4. 55.5 x 1.5 + 4 = 87.25, matching the fifth term.

5. 87.25 x 1.5 + 5 = 135.875, matching the sixth term.

6. 135.875 x 1.5 + 6 = 209.8125, matching the seventh term.

Cross-check: Every term after the second one reproduces exactly when the rule is applied to the corrected running value, confirming no other term is out of place.

Hence, 34.5 is the wrong number in the series; it should have been 35.